Adaptive fuzzy optimal control for a class of active suspension systems with full‐state constraints

In this study, an adaptive fuzzy inverse optimal control problem is investigated for a class of vehicle active suspension systems. Since active suspension systems have dynamic characteristics of complexities and spring non-linearities, the fuzzy logic systems are utilised to learn the unknown non-linear dynamics. In addition, there exist the constraints of the displacements of the sprung and unsprung masses, vertical vibration speeds, and current intensity in the considered suspension system, therefore, the Barrier Lyapunov functions are introduced into the control design to ensure that the full-state constraints are not overstepped. The inverse optimal control method is adopted by constructing an auxiliary system, which circumvents the assignment of solving a Hamilton–Jacobi–Bellman equation and brings about an inverse optimal controller associated with a meaningful objective functional. Based on Lyapunov stability theory and backstepping recursive design algorithm, a fuzzy adaptive optimal control scheme is developed. It is proved that the proposed control scheme not only guarantees that the vertical vibration of the vehicle is stabilised by the electromagnetic actuator but also achieves the goal of inverse optimality with regard to the cost functional. Finally, the simulation studies check the validity of the presented control strategy.

[1]  Marios M. Polycarpou,et al.  Command filtered backstepping , 2009, 2008 American Control Conference.

[2]  Shaocheng Tong,et al.  Finite-Time Filter Decentralized Control for Nonstrict-Feedback Nonlinear Large-Scale Systems , 2018, IEEE Transactions on Fuzzy Systems.

[3]  Xin Zhang,et al.  Data-Driven Robust Approximate Optimal Tracking Control for Unknown General Nonlinear Systems Using Adaptive Dynamic Programming Method , 2011, IEEE Transactions on Neural Networks.

[4]  Shiuh-Jer Huang,et al.  Adaptive sliding controller with self-tuning fuzzy compensation for vehicle suspension control , 2006 .

[5]  Shuzhi Sam Ge,et al.  Adaptive Fuzzy Control of a Class of Nonlinear Systems by Fuzzy Approximation Approach , 2012, IEEE Transactions on Fuzzy Systems.

[6]  Jing Na,et al.  Nonlinear Constrained Optimal Control of Wave Energy Converters With Adaptive Dynamic Programming , 2019, IEEE Transactions on Industrial Electronics.

[7]  Zhigang Zeng,et al.  Fuzzy Control for Uncertain Vehicle Active Suspension Systems via Dynamic Sliding-Mode Approach , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[8]  Mihalis Yannakakis,et al.  Markov Decision Processes and Regular Events (Extended Abstract) , 1990, ICALP.

[9]  Petar V. Kokotovic,et al.  Locally optimal and robust backstepping design , 2000, IEEE Trans. Autom. Control..

[10]  Shaocheng Tong,et al.  Fuzzy-Adaptive Decentralized Output-Feedback Control for Large-Scale Nonlinear Systems With Dynamical Uncertainties , 2010, IEEE Transactions on Fuzzy Systems.

[11]  Ka C. Cheok,et al.  Model reference adaptive control for vehicle active suspension systems , 1991 .

[12]  Euntai Kim,et al.  Output feedback tracking control of MIMO systems using a fuzzy disturbance observer and its application to the speed control of a PM synchronous motor , 2005, IEEE Trans. Fuzzy Syst..

[13]  Shaocheng Tong,et al.  Observer-based fuzzy adaptive control for strict-feedback nonlinear systems , 2009, Fuzzy Sets Syst..

[14]  Guido Herrmann,et al.  Active Adaptive Estimation and Control for Vehicle Suspensions With Prescribed Performance , 2018, IEEE Transactions on Control Systems Technology.

[15]  Qiao Zhu,et al.  A Low-Cost Lateral Active Suspension System of the High-Speed Train for Ride Quality Based on the Resonant Control Method , 2018, IEEE Transactions on Industrial Electronics.

[16]  Hak-Keung Lam,et al.  Fuzzy Sampled-Data Control for Uncertain Vehicle Suspension Systems , 2014, IEEE Transactions on Cybernetics.

[17]  Shaocheng Tong,et al.  Fuzzy Adaptive Finite-Time Control Design for Nontriangular Stochastic Nonlinear Systems , 2019, IEEE Transactions on Fuzzy Systems.

[18]  D. Hrovat,et al.  Survey of Advanced Suspension Developments and Related Optimal Control Applications, , 1997, Autom..

[19]  Fan Yu,et al.  Predictive controller design for electromagnetic suspension based on mixed logical dynamical model , 2012 .

[20]  Honghai Liu,et al.  An Interval Fuzzy Controller for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Intelligent Transportation Systems.

[21]  Ruey-Jing Lian,et al.  Intelligent Control of Active Suspension Systems , 2011, IEEE Transactions on Industrial Electronics.

[22]  M. Krstić,et al.  Inverse optimal design of input-to-state stabilizing nonlinear controllers , 1998, IEEE Trans. Autom. Control..

[23]  Huijun Gao,et al.  Robust Sampled-Data $H_{\infty}$ Control for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Control Systems Technology.

[24]  Huaguang Zhang,et al.  Near-Optimal Control for Nonzero-Sum Differential Games of Continuous-Time Nonlinear Systems Using Single-Network ADP , 2013, IEEE Transactions on Cybernetics.

[25]  Gary J. Balas,et al.  Road adaptive active suspension design using linear parameter-varying gain-scheduling , 2002, IEEE Trans. Control. Syst. Technol..

[26]  Xiangpeng Xie,et al.  Adaptive Event-Triggered Fuzzy Control for Uncertain Active Suspension Systems , 2019, IEEE Transactions on Cybernetics.

[27]  Huijun Gao,et al.  Finite-Time Stabilization for Vehicle Active Suspension Systems With Hard Constraints , 2015, IEEE Transactions on Intelligent Transportation Systems.

[28]  Jing Na,et al.  Approximation-Free Control for Vehicle Active Suspensions With Hydraulic Actuator , 2018, IEEE Transactions on Industrial Electronics.

[29]  Jianbin Qiu,et al.  Adaptive Fuzzy Control for Nontriangular Structural Stochastic Switched Nonlinear Systems With Full State Constraints , 2019, IEEE Transactions on Fuzzy Systems.

[30]  Malcolm C. Smith,et al.  Linear Quadratic Optimal and Risk-Sensitive Control for Vehicle Active Suspensions , 2014, IEEE Transactions on Control Systems Technology.

[31]  Sahin Yildirim,et al.  Vibration control of vehicle active suspension system using a new robust neural network control system , 2009, Simul. Model. Pract. Theory.

[32]  Mehdi Soleymani,et al.  Investigation of the Energy Regeneration of Active Suspension System in Hybrid Electric Vehicles , 2010, IEEE Transactions on Industrial Electronics.

[33]  Yifu Zhang,et al.  Multi-objective control for uncertain nonlinear active suspension systems , 2014 .

[34]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[35]  Shaocheng Tong,et al.  A Combined Backstepping and Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2009, IEEE Transactions on Fuzzy Systems.

[36]  Huijun Gao,et al.  Active Suspension Control With Frequency Band Constraints and Actuator Input Delay , 2012, IEEE Transactions on Industrial Electronics.

[37]  Huijun Gao,et al.  Adaptive Backstepping Control for Active Suspension Systems With Hard Constraints , 2013, IEEE/ASME Transactions on Mechatronics.

[38]  Dae Sung Joo,et al.  Sliding mode neural network inference fuzzy logic control for active suspension systems , 2002, IEEE Trans. Fuzzy Syst..

[39]  Shrivijay B. Phadke,et al.  Nonlinear Control for Dual Objective Active Suspension Systems , 2017, IEEE Transactions on Intelligent Transportation Systems.

[40]  Shaocheng Tong,et al.  Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints , 2016, Autom..

[41]  Ramin Amirifar,et al.  Low-order H/sub /spl infin// controller design for an active suspension system via LMIs , 2006, IEEE Transactions on Industrial Electronics.

[42]  P. Kokotovic,et al.  Inverse Optimality in Robust Stabilization , 1996 .