本論文針對四種常見的非自主系統(non-autonomous system)，進行其適應控制研究。由於考慮之系統皆具有時變不確定性(uncertainty)，且不確定性的變化邊界亦非全為已知，因此傳統適應控制方法以及強健控制理論都無法直接使用。對此，本文提出兩種以函數近似為基礎之適應控制器來解決不確定系統之輸出追蹤問題。發展之控制器也將應用於液壓主動式懸吊系統，以改善駕駛乘坐舒適度及避免懸吊過度變形所發生之碰撞(bottoming out)問題。為說明上述之研究，我們將論文分成兩大部分，第一部份針對不確定系統推導適應控制器，第二部份則利用提出之控制器達成主動懸吊系統的設計需求。

第一部份首先探討單輸入單輸出(single-input single-output)系統之控制問題。為處理系統中的匹配不確定性(matched uncertainty)，我們先將此不確定性視為未知的連續函數，並利用函數近似法(function approximation technique, FAT) 將其展開成正交級數的線性組合，進而推導一函數估測器(簡稱 FAT 估測器)以完成適應控制器設計(adaptive tracking controller, ATC)。其後我們考慮不確定性之非匹配問題(mismatch problem)，並引入多面設計的技巧發展出一適應多面追蹤控制器(adaptive multiple-surface tracking controller, AMSTC)，其中各滑動面間的未知函數仍舊是利用 FAT 估測器進行處理。此法有別於使用狀態相依模型(state-dependent approximation model, 如類神經網路或模糊系統)所發展之控制器，是利用時變基底函數來建構函數估測器，因此不受限於 strict-feedback 或 pure-feedback 等系統限制，大大改善了多數 FAT 適應控制方法之問題。

本論文亦嘗試將上述的控制器(ATC 及 AMSTC)推展至多輸入多輸出(multi-input multi-output, MIMO)系統。由於此種系統有著複雜的狀態連結(interconnection)，且其子系統間的輸入常具有耦合特性(input coupling)，若再加上不確定性的影響，則控制問題將變得十分困難。為克服上述問題，延伸之 ATC 仍舊利用 FAT 估測器來處理各個子系統的匹配未知函數，而輸入耦合矩陣(input-coupling matrix)內的不確定性則是利用強健控制的技巧加以處理，若矩陣內不確定性之變動邊界能進一步求得，則控制輸入之奇異問題(singularity problem)便可有效解決。此部份最後考慮 MIMO 非匹配系統之控制問題，由於該系統是由一組 “perturbed chain-of integrator” 子系統所組成，其複雜度更甚於 block-triangular 系統，至今仍少有文獻加以探討。對此，我們結合了 MIMO 之 ATC以及 AMSTC 方法發展一系統化的設計，用以達各個子系統之輸出追蹤控制。

為確保閉迴路系統穩定度，上述的控制器設計皆輔有 Lyapunov 穩定性分析，而對於函數近似誤差之影響，文中亦有詳細探討。此外，本論文也將分析追蹤誤差的暫態邊界(upper bounds of tracking errors in the transient state)，藉此確保暫態控制性能。

在第二部份，我們著手處理四分之一車之主動式懸吊系統控制問題。文中考慮的懸吊系統具有未知時變車重、車體外部干擾以及被動元件之未知物理特性。由於有部份的系統不確定性為時變且其變化邊界亦無法求得，因此傳統的適應控制及強健控制理論並不適用。在此，我們利用第一部份發展之 ATC 來處理車體之動態行為，藉由讓車體追蹤事先規劃之平滑軌跡以改善乘坐舒適度，若此軌跡可另依據懸吊系統變形或輪胎變形而作適當修整，便可兼顧車輛操控性及抓地力等其他需求。本文以乘坐舒適度為設計首要目標，另亦考慮車輛行駛時可能發生之懸吊系統過度變形問題，由於阻尼器(或彈簧)之行程有限，過量的懸吊拉伸或收縮都將導致阻尼器之活塞撞擊其末端缸壁，而此種碰撞將使乘客產生極大的不適感。為避免此種問題，我們引入一非線性參考模型來產生車體理想軌跡，此模型在懸吊系統變形較小時，輸出較平滑的軌跡以改善乘坐舒適度，當懸吊變形量過大時，便修正軌跡以減少車體與輪胎間的相對位移量。

為實現計算之控制力，本文亦考慮液壓制動器之動態特性。首先，我們針對制動器模型內的未知時變參數進行處理，並設計一 ATC 以完成力量追蹤控制。其後，此制動器模型將與上述之懸吊模型一併探討，為同時處理系統內的匹配以及非匹配不確定性(分別存在於制動器模型以及懸吊系統模型內)，我們使用 AMSTC 方法。此處的控制目標仍舊與無考慮制動器動態時相同，先是控制車體輸出使其收斂至理想運動軌跡，再與參考模型結合以完成總體設計。

由於此部份之研究是植基於第一部份的成果，因此對於追蹤誤差動態皆有嚴謹的穩定度分析，此外，文中對於控制器未處理之內部動態(internal dynamics)也有進一步的分析與探討。最終，本文將以電腦模擬驗證控制器的功效與可行性。

This dissertation addresses the problem of controlling four classes of non-autonomous systems containing general uncertainties (i.e., unknown time-varying nonlinearities without available variation bounds) with investigations to the design of hydraulic active suspension systems (ASS). Owing to the presence of the general uncertainties in the system dynamics, traditional adaptive schemes or robust control strategies are not applicable. To deal with this problem, this dissertation proposes several stable adaptive controllers based on function approximation technique (FAT), some of which are then applied to the ASS. Therefore, this dissertation is organized into two parts: Part 1 develops the FAT based adaptive control theory and Part 2 presents the control of ASS using FAT based adaptive controllers.

In Part 1, we first derive a FAT based adaptive tracking controller for a class of matched single-input single-output (SISO) non-autonomous systems with general uncertainties. The FAT is used to construct approximation models for uncertainties, so that their update laws can be chosen from the conventional Lyapunov-like design to ensure the closed-loop stability. Different from the approaches using state-dependent approximation models (SDAM), such as neural networks or fuzzy systems, here we employ time-dependent orthogonal basis functions to be the approximator. By utilizing the proposed controller, uniformly ultimate boundedness of the closed-loop system can be arrived at along with guaranteed transient-state performance. Afterwards, we consider a class of uncertain SISO systems in “perturbed chain-of-integrator” form. Since the structure of the system is much more complicated than that in strict-feedback or pure-feedback form, most of SDAM based backstepping designs are infeasible. To deal with the problem, this dissertation proposes an adaptive multiple-surface tracking (AMST) controller, where the multiple-surface design is used to cope with the uncertainty mismatch problem and the uncertainties in each error surface are still tackled by the FAT based function estimators (consisting of time-dependent approximators with proper update laws). Because of the state independence of the approximators, the real control input will not appear until the last step of the derivation comes up. Hence, the pure-feedback restriction can be completely removed. Uniformly ultimately bounded performance is still obtained by means of the AMST design. In addition, explicit upper bound for the error signals of each error surface is acquired with adjustable size to avoid unwanted peaking phenomenon.

The result of the adaptive tracking controller (in matched SISO case) is then extended to a matched MIMO square system whose subsystems are of different block sizes. By utilizing the extended controller to cope with the matched uncertainties in each and every subsystem, similar performance result as in SISO counterpart is guaranteed. At the end of Part 1, the AMST method is combined with the extended adaptive tracking controller to form a systematic design procedure for a mismatched MIMO square system composed of several perturbed chain-of-integrator subsystems with full interconnection among each other. This system is beyond the assumption of “block-triangular” form and the combination provides an effective tool to deal with its control problem. The closed-loop system with the extended ASMT controller can be shown to be uniformly ultimately bounded and the transient performance can be also ensured.

In spite of the above development, an important issue to be considered in implementing the control laws is the “singular problem”. To avoid this problem, in the proposed designs, the input-channel uncertainties are suppressed by employing a robust control term with additional assumption that the bounds of the input-channel uncertainties (or input-channel uncertainty matrix in MIMO cases) are available. Modifications for the term to be feasible in either SISO or MIMO case are made in this dissertation with statements to the required conditions.

In Part 2, we proceed to investigate the control of a non-autonomous quarter-car ASS with uncertain passive components, unknown car-body loads, and external disturbances on the car-body part. Since most of these uncertainties are of unknown bounds and some of them yet possess time-varying nature, the ASS designs based on traditional adaptive schemes or robust strategies are infeasible. The FAT based adaptive tracking controller is thus applied to deal with the uncertain car-body dynamics, so that the car-body motion can be convergent to some pre-described desired trajectories. Afterwards, a nonlinear filter is introduced into the control loop to generate the car-body desired trajectory, which is able to switch the objective between ride comfort and suspension travel according to the current suspension deflection.

To realize the control force, a hydraulic actuator is employed with consideration to its uncertain dynamics. The FAT based adaptive tracking controller is again used to achieve the force tracking of the actuator. Then, the actuator model is combined with the uncertain ASS to form a full-blown model of the quarter-car hydraulic ASS. In order to cope with both of the matched (in actuator part) and the mismatched (in suspension part) uncertainties, an AMST controller is derived. The objective is the same as in the case without actuator to accomplish the tracking control of the car-body motion with incorporation of the nonlinear filter. The closed-loop stability (including the internal dynamics) is ensured via the Lyapunov analysis and computer simulations are performed to verify the effectiveness of the proposed methods.

[1] A. Isidori, Nonlinear Control Systems: An Introduction, 2nd Edition, Springer-Verlag, 1989.
[2] K. Zhou and J. C. Doyle, Essentials of Robust Control, Prentice Hall, New Jersey, 1998.
[3] J.-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, New Jersey, 1991.
[4] Y. S. Kuo, A Study of Adaptive Control for Uncertain Non-autonomous Systems, Ph.D. Dissertation, National Taiwan University of Science and Technology, Taiwan, 2002. (In Chinese)
[5] A. C. Huang and Y. S. Kuo, “Sliding control of nonlinear systems containing time-varying uncertainties with unknown bounds,” International Journal of Control, Vol. 74, No. 3, pp. 252-264, 2001.
[6] A. C. Huang and Y. S. Kuo, “A model reference adaptive control scheme for uncertain non-autonomous system,” Journal of the Chinese Society of Mechanical Engineers, Vol. 22, No. 6, pp. 537-544, 2001.
[7] A. C. Huang and Y. C. Chen, “Adaptive multiple-surface sliding control for single-link flexible-joint robot with mismatched uncertainties,” IEEE Transactions on Control Systems Technology, Vol. 12, No. 5, pp. 770-775, 2004.
[8] A. C. Huang and Y. C. Chen, “Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties,” Automatica, Vol. 11, No. 40, pp. 1939-1945, 2004, 2004.
[9] J. T. Spooner, M. Maggiore, R. Ordonez and K. M. Passino, Stable Adaptive Control and Estimation for Nonlinear Systems – Neural and Fuzzy Approximator Techniques, John Wiley and Sons, New York, 2002.
[10] J. T. Spooner and K. M. Passino, “Stable adaptive control using fuzzy systems and neural networks,” IEEE Transactions on Fuzzy System, Vol. 4, No. 3, pp. 339-356, 1996.
[11] J. T. Spooner and K. M. Passino, “Adaptive control of a class of decentralized nonlinear system,” IEEE Transactions on Automatic Control, Vol. 41, No. 2, pp. 280-284, 1996.
[12] R. Ordonez and K. M. Passino, “Stable multi-input multi-output adaptive fuzzy/neural control,” IEEE Transactions on Fuzzy System, Vol. 7, No. 3, pp. 345-353, 1999.
[13] S. S. Ge, C. C. Hang, T. H. Lee and T. Zhang, Stable Adaptive Neural Network Control, Kluwer Academic Publishers, 2002.
[14] S. S. Ge, C. C. Hang and T. Zhang, “A direct method for robust adaptive nonlinear control with guaranteed transactionsactionsient performance,” Systems and Control Letters, Vol. 37, pp. 275-284, 1999.
[15] S. S. Ge, C. C. Hang and T. Zhang, “Stable adaptive control for nonlinear multivariable systems with a triangular control structure,” IEEE Transactions on Automatic Control, Vol. 45, No. 6, pp. 1211-1225, 2000.
[16] S. S. Ge and C. Wang, “Direct adaptive NN control of a class of nonlinear systems,” IEEE Transactions on Neural Networks, Vol. 13, No. 1, pp. 214-221, 2002.
[17] S. S. Ge and C. Wang, “Adaptive NN control of uncertain nonlinear pure-feedback systems,” Automatica, Vol. 38, No. 4, pp.671-682, 2002.
[18] S. S. Ge and C. Wang, “Adaptive neural control of uncertain MIMO nonlinear systems,” IEEE Transactions on Neural Networks, Vol. 15, No. 3, pp. 674-692, 2004.
[19] M. M. Polycarpou, “Stable adaptive NN control scheme for nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 41, No. 3, pp. 447-451, 1996.
[20] A. Yesidirek and F. L. Lewis, “Feedback linearization using neural networks,” Automatica, Vol. 31, No. 11, pp. 1659-1664, 1995.
[21] E. B. Kosmatopoulos, “Universal stabilization using control Lyapunov functions, adaptive derivative feedback and neural network approximators,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, Vol. 28, No. 3, pp.472-477, 1998.
[22] F. C. Chen and C. C. Liu, “Adaptive controlling nonlinear continuous-time systems using multilayer neural networks,” International Journal of Control, Vol. 58, No.2, pp. 317-335, 1994.
[23] R. M. Sanner and J. J. Slotine, “Caussian networks for direct adaptive control,” IEEE Transactions on Neural Networks, Vol. 3, No. 6, pp. 837-863, 1992.
[24] P. A. Ioannou and J. Sun, Robust Adaptive Control, Prentice-Hall, Englewood Cliff, 1995.
[25] S. Gutman, “Uncertain dynamical systems: a Lyapunov min-max approach,” IEEE Transactions on Automatic Control, Vol.24, pp.437-443, 1979.
[26] G. Leitmann, “Guaranteed asymptotic stability for some linear systems with bounded uncertainties,” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, Vol.101, pp.212-216, 1979.
[27] Y. H. Chen and G. Leitmann, “Robustness of uncertain systems in the absence of matching assumptions,” International Journal of Control, Vol. 45, No. 5, pp.1527-1542, 1987.
[28] M. Krstic, I. Kanellakopoulos and P. V. Kokotovic, Nonlinear and Adaptive control design, John Wiley and Sons, 1995.
[29] I. Kanellakopoulos, P. V. Kokotovic and R. Marino, “An extended direct scheme for robust adaptive nonlinear control,” Automatica, Vol. 27, No. 2, pp. 247-288, 1991.
[30] I. Kanellakopoulos, P. V. Kokotovic and A. S. Morse, “Systematic design of adaptive controllers for feedback linearizable system,” IEEE Transactions on Automatic Control, Vol. 36, No. 11, pp. 1241-1252, 1991.
[31] P. V. Kokotovic, “The joy of feedback: nonlinear and adaptive,” IEEE Control Systems Magazine, Vol. 12, pp. 7-17, 1991.
[32] M. Kristic, I. Kanellakopoulos and P. V. Kokotovic, “Adaptive nonlinear control without over-parameterization,” Systems and Control Letters, Vol. 19, pp. 177-185, 1992.
[33] R. A. Freeman and P. V. Kokotovic, “Design of softer robust nonlinear control laws”, Automatica, Vol. 29, pp. 1425-1437, 1993.
[34] M. M. Polycarpou and P. A. Ioannou, “A Robust adaptive nonlinear control design,” Automatica, Vol. 32, No. 3, pp. 423-427, 1996.
[35] B. Yao and M. Tomizuka, “Adaptive robust control of SISO nonlinear systems in a semi-strict feedback form,” Automatica, Vol. 3, No. 5, pp, 893-900, 1997.
[36] Z. Pan and T. Basar, “Adaptive controller design for tracking and disturbance attenuation in parametric strict-feedback nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 43, No. 8, pp. 1066-1083, 1998.
[37] F. Giri, A. Rabeh and F. Ikhouane, “Backstepping adaptive control of time-varying plants,” Systems and Control Letters, Vol. 36, pp. 245-252, 1999.
[38] Z. P. Jiang, “A combined backstepping and small-gain approach to adaptive output feedback control,” Automatica, Vol. 35, pp. 1131-1139, 1999.
[39] A. J. Koshkouei and A. S. I. Zinober, “Adaptive backstepping control of nonlinear systems with unmatched uncertainty,” Proceeding of IEEE Conference on Decision and Control, pp. 4765-4769, 2000.
[40] M. Won and J. K. Hedrick, “Multiple-surface sliding control of a class of uncertain nonlinear systems”, International Journal of Control, Vol.64, No.46, pp.693-706, 1996.
[41] P. P. Yip and J. K. Hedrick, “The use of sliding modes to simplify the backstepping control method,” Proceedings of American Control Conference, pp.1703-1708, 1997.
[42] P. P. Yip, Robust and Adaptive Nonlinear Control Using Dynamic Surface Controller with Applications to Intelligent Vehicle Highway Systems, Ph. D Dissertation, University of California at Berkeley, Berkeley, CA, 1997.
[43] D. Swaroop, J. K. Hedrick, P. P. Yip, and J. C. Gerdes, “Dynamic surface control of nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 45, No. 10, pp. 1893-1899, 2000.
[44] B. Song, J. K. Hedrick and A. Howell, “Robust stabilization and ultimate boundedness of DSC via convex optimization,” International Journal of Control, Vol. 75, No. 12, pp. 870-881, 2002.
[45] D. H. McMahon, J. K. Hedrick and S. E. Shladover, “Vehicle modeling and control for automated highway systems,” Proceeding of American Control Conference, pp. 297-303, 1990.
[46] J. H. Green and K. Hedrick, “Nonlinear Speed Control of Automotive Engines,” Proceeding of the American Control Conference, pp. 2891-2897, 1990.
[47] J. C. Gerdes and J. K. Hedrick, “Vehicle speed and spacing control via coordinated throttle and brake actuation,” Control Engineering Practice, Vol. 5, No. 11, pp. 1607-1614, 1997.
[48] M. M. Ploycarpou and M. J. Mears, “Stable adaptive tracking of uncertain systems using nonlinearly parameterized on-line approximators,” International Journal of Control, Vol. 74, No. 3, pp. 363-384, 1998.
[49] Y. Zhang, “Stable neural controller design for unknown nonlinear systems using backstepping,” IEEE Transactions on Neural Networks, Vol. 11, No. 6, pp. 1347-1360, 2000.
[50] D. Seto, M. Annaswany and J. Bailleul “Adaptive control of nonlinear systems with a triangular structure,” IEEE Transactions on Automatic Control, Vol. 39, No. 7, pp. 1411-1428, 1994.
[51] L. Karsenti, F. Lamnabhi-Lagarrigue and G. Bastin, “Adaptive control of nonlinear systems with nonlinear parameterization,” Systems and Control Letters, Vol. 27, pp. 87-97, 1996.
[52] G. Bartolini, A. Ferrara and L. Giacomin, “A robust control design for a class of uncertain nonlinear systems featuring a second-order sliding mode,” International Journal of Control, Vol. 72, No. 4, pp. 321-331, 1999.
[53] F. C. Chen and H. K. Khalil, “Adaptive control of a class of nonlinear discrete-time systems using neural networks,” IEEE Transactions on Automatic Control, Vol. 40, No. 5, pp. 791-801, 1995.
[54] H. G. Zhang, L. L. Cai and Z. G. Bien, “A fuzzy function vector-based multivariable adaptive controller for nonlinear systems,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 30, No. 1, pp. 210-217, 2000.
[55] H. Xu and P. A. Ioannou, “Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds,” IEEE Transactions on Automatic Control, Vol. 48, No. 5, pp. 728-742, 2003.
[56] S. Jain and F. Khorrami, “Decentralized adaptive control of a class of large-scale interconnected nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 42, No. 2, pp. 136-154, 1997.
[57] K. Nam and A. Arapostathis, “A model reference adaptive control scheme for pure-feedback nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 33, No. 9, pp. 803-811, 1988.
[58] E. B. Kosmatopoulos and P. A. Ioannou, “Robust switching control of MIMO nonlinear systems,” IEEE Transactions on Automatic Control, Vol. 47, No. 4, pp.610-623, 2002.
[59] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1976.
[60] S. Gopalswamy and J. K. Hedrick, “Robust adaptive control of multivariable nonlinear systems,” Proceeding of American Control Conference, pp. 2247-2252, 1990.
[61] J. K. Hedrick and S. Gopalswamy, “Nonlinear flight control design via sliding methods,” Journal of Guidance, Control and Dynamics, Vol. 13, No.5, pp. 850-858, 1990.
[62] C. Kwan and F. L. Lewis, “Backstepping control of nonlinear systems using neural networks,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 30, No. 6, pp. 753-766, 2000.
[63] P. C. Chen and A. C. Huang, “Adaptive tracking control for a class of non-autonomous systems containing time-varying uncertainties with unknown bounds,” Proceeding of IEEE International Conference on Systems, Man and Cybernetics, pp. 5870-5875, 2004.
[64] P. C. Chen and A.C. Huang, “Adaptive multiple-surface sliding control of active suspension systems with mismatched uncertainties,” submitted to IEEE Transactions on Control Systems Technology. (Under revision)
[65] H. K. Khalil, Nonlinear Systems, 3rd Edition, Prentice-Hall, New Jersey, 2002.
[66] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, New Jersey, 2002.
[67] C. Kwan and F. L. Lewis, “Backstepping control of induction motors using neural networks,” IEEE Transactions on Neural Networks, Vol. 11, No. 5, pp. 1179-1187, 2000.
[68] G. Genta, Motor Vehicle Dynamics: Modeling and Simulation, World Scientific, 1997.
[69] M. Tomizuka and J. K. Hedrick, “Advanced control methods for automotive applications, ” Vehicle System Dynamics, Vol. 24, pp. 449-468, 1995.
[70] D. Hrovat, “Survey of advanced suspension developments and related optimal control applications,” Automatica, Vol. 33, No. 10, pp. 1781-1817, 1997.
[71] A. Baker, “Lotus active suspension,” Automotive Engineer, Vol. 9, No. 1, pp.56-57, 1984.
[72] C. Yue, T. Butsuen and J. K. Hedrick, “Alternative control laws for automotive active suspensions,” ASME Journal of Dynamic Systems, Measurement and Control, Vol. 111, No. 2, pp. 286-291, 1989.
[73] D. Karnopp, “Active and semi-active vibration isolation,” ASME Journal of Mechanical Design, Vol. 117, pp. 177-185, 1995.
[74] D. Hrovat, “Optimal active suspension structures for quarter-car vehicle models,” Automatica, Vol. 26, No. 5, pp. 845-860, 1990.
[75] M, Tomizuka, “Optimal continuous finite preview problem,” IEEE Transactions on Automatic Control, Vol. AC-20, No. 3, pp. 362-365, 1975.
[76] M. Tomizuka and D. E. Rosenthal, “On the optimal digital state vector feedback controller with integral and preview actions,” ASME Journal of Dynamic Systems, Measurement and Control, Vol. 101, No. 2, pp. 162-171, 1979.
[77] M. Tomizuka, “Optimum linear preview control with application to vehicle suspension - revisited,” Journal of Dynamic Systems, Measurement and Control, Transactions ASME, Vol. 98, No. 3, pp. 309-315, 1976.
[78] E. K. Bender, “Optimum linear preview control with application to vehicle suspension,” ASME Journal of Basic Engineering, Vol. 90, No. 2, pp. 213-221, 1968.
[79] A. G. Thompson, B. R. Davis, and C. E. M. Pearce, “An optimal linear active suspension with finite road preview,” SAE paper, No. 800520, 1980.
[80] A. Hac, “Optimal linear preview control of active vehicle suspension,” Vehicle System Dynamics, Vol. 21, pp. 167-195, 1992.
[81] C. Kim and P. I. Ro, “A sliding mode controller for vehicle active suspension systems with non-linearities,” Proc. IME, Journal of Automobile Engineering, Vol. 212, No. D2, pp. 79-92, 1998.
[82] T. Yoshimura, A. Kume, M. Kurimoto and J. Hino, “Construction of an active suspension system of a quarter car model using the concept of sliding mode control,” Journal of Sound and Vibration, Vol. 239, No. 2, pp. 187-199, 2001.
[83] M. Sunwoo, K.C. Cheok and N.J. Huang, “Model reference adaptive control for vehicle active suspension systems,” IEEE Transactions on Industrial Electronics, Vol. 38, No. 3, pp. 217-222, 1991.
[84] P. C. Chen and A. C. Huang, “Adaptive sliding control of non-autonomous active suspension systems with time-varying loadings,” Journal of Sound and Vibration, Vol. 282, No. 3-5, pp. 1119-1135, 2005.
[85] F. C. Wang and M. C. Smith, “Disturbance response decoupling and achievable performance with application to vehicle active suspension,” International Journal of Control, Vol. 75, No. 12, pp. 946-953, 2002.
[86] M. C. Smith and F. C. Wang, “Controller parameterization for disturbance response decoupling: application to vehicle suspension control,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 3, pp. 393-407, 2002.
[87] J. Wang and D. A. Wilson, “Mixed control with pole placement and its application to vehicle suspension systems,” International Journal of Control, Vol. 74, No. 13, pp. 1353-1396, 2001.
[88] A. G. Thompson and P. M. Chaplin, “Force control in electro-hydraulic active suspensions,” Vehicle System Dynamics, Vol. 25, pp. 185-202, 1996.
[89] A. Alleyne, R. Liu and H. Wright, “On the limitations of force tracking control for hydraulic active suspension,” Proceedings of American Control Conference, pp. 43-47, 1998.
[90] J. S. Lin and I. Kanellakopoulos, “Nonlinear design of active suspensions,” IEEE Control Systems Magazine, Vol. 17, No. 3, pp. 45-59, 1997.
[91] N. Karlsson, A. Teel and D. Hrovat, “A backstepping approach to control of active suspension,” Proceeding of IEEE Conference on Decision and Control, pp. 4170-4175, 2001.
[92] I. Fialho and G. J. Balas, “Road adaptive active suspension design using linear parameter-varying gain-scheduling,” IEEE Transactions on Control Systems Technology, Vol. 10, No. 1, pp. 43-54, 2002.
[93] H. D. Tuan, E. Ono, P. Apkarian and S. Hosoe, “Nonlinear control for an integrated suspension system via parameterized linear matrix inequality characterizations,” IEEE Transactions on Control Systems Technology, Vol. 9, No. 1, pp. 175-185, 2001.
[94] A. Alleyne and J. K. Hedrick, “Nonlinear adaptive control of active suspensions,” IEEE Transactions on Control Systems Technology, Vol. 3, No. 1, pp. 94-101, 1995.
[95] E. S. Kim, “Nonlinear indirect adaptive control of a quarter car active suspension,” Proceeding of IEEE International Conference on Control Applications, pp. 61-66, 1996.
[96] P. C. Chen and A. C. Huang, “Adaptive sliding control of active suspension systems with uncertain hydraulic actuator dynamics,” Vehicle System Dynamics, in press.
[97] P. C. Chen and A. C. Huang, “Adaptive multiple-surface sliding control of hydraulic active suspension systems based on function approximation technique,” Journal of Vibration and Control, Vol. 11, pp. 685-706, 2005.
[98] S. Chantranuwathana and H. Peng, “Force tracking control for active suspensions - theory and experiments,” Proceedings of IEEE International Conference on Control Applications, pp. 442-447, 1999.
[99] S. Chantranuwathana and H. Peng, “Adaptive robust force control for vehicle active suspensions,” Internal Journal of Adaptive Control and Signal Processing, Vol. 18, No. 2, pp. 83-102, 2004.
[100] T. Fukao, A. Yamawaki and N. Adachi, “Adaptive control of partially known systems and application to active suspensions,” Asian Journal of Control, Vol. 4, No. 2, pp.199-205, 2002.
[101] T. T. Nguyen, T. H. Bui, T. P. Tran and S. B. Kim, “A hybrid control of active suspension system using and nonlinear adaptive controls,” Proceeding of International Symposium on Industrial Electronics, Vol. 2, pp. 839-844, 2001.
[102] D. Karnopp, “Theoretical limitations in active vehicle suspensions”, Vehicle System Dynamics, Vol. 15, pp. 41-54, 1986.
[103] J. K. Hedrick and T. Butsuen, “Invariant properties of automotive suspensions,” Proceedings of Institution of Mechanical Engineering, Vol. 204, pp. 21-27, 1990.
[104] K. Ogata, Modern Control Engineering, 4th edition, Prentice-Hall, 2002.
[105] F. L. Lewis and V. L. Syrmos, Optimal control, 2nd edition, John Wiley and Sons, 1995.
[106] C. T. Chen, Linear System Theory and Design, 3rd edition, Oxford, 1999.
[107] M. Yamashita, K. Fujimori, K. Hayakawa and J. H. Kimura, “Application of H control to active suspension systems,” Automatica, Vol. 30, No. 11, pp. 1717-1729, 1994.
[108] J. Y. Wang, Theory of Ground Vehicles, 2nd edition, John Wiley and Sons, 1993.
[109] H. E. Merrit, Hydraulic Control Systems, John Wiley and Sons, New York, 1967.
[110] H. Lutkepohl, Handbook of Matrices, John Wiley and Sons, 1997.
[111] D. G Luenberger, Introduction to Dynamic Systems, Wiley, New York, 1979.