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Stackelberg Game Approach to Mixed H2/H∞ Problem for Continuous-Time System

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Journal of Systems Science & Complexity 2019年第5期32卷 1324-1339页

作者： LI Xiaoqian WANG Wei XU Juanjuan ZHANG Huanshui School of control Science and engineering Shandong University

This paper studies the mixed H2/H∞ control for continuous-time linear dynamic *** applying Stackelberg game approach, the control input is treated as the leader and the disturbance is treated as the follower, respectively. Under standard assumptions and maximum principle, a necessary and sufficient existence condition which is based on three decoupled Riccati equations is *** expression of controllers and solutions to forward backward differential equations(FBDES)are obtained by homogeneous analysis of variables. A numerical example is finally given to verify the efficiency of the proposed approach.

关键词： Continuous-time case mixed H2/H∞ control open-loop controller Stackelberg game approach

Global adaptive output-feedback tracking with prescribed performance for uncertain nonlinear systems

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Science China(Information Sciences) 2024年第5期67卷 150-164页

作者： Yuan WANG Yungang LIU School of control Science and engineering Shandong University

At present, one typical control strategy for guaranteeing transient and steady-state performance is funnel control and prescribed performance control. The strategy features completely discarding the system nonlinearities, even if they are completely known and available. Such an intrinsic feature requires the controller to produce a larger control effect to eliminate the negative impact caused by the high nonlinearities, leading to a conservative controller. In this paper, we fully take advantage of known information on nonlinearities in control design, instead of completely discarding it as done in funnel control. Particularly, we leverage adaptive techniques(i.e., high-gain dynamic compensation) to deal with unknown system nonlinearities. Meanwhile, we integrate the tools of output feedback, tracking control, and the performance *** such, an adaptive output-feedback scheme is developed for global tracking with spatiotemporal performance specifications: arbitrarily given tracking accuracy and accuracy-ensured time. A simulation example supports the developed approach.

关键词： uncertain nonlinear systems output feedback prescribed performance unknown control direction dynamic high gain global tracking

Structural Synthesis of Parallel Mechanisms with High Rotational Capability

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Chinese Journal of Mechanical engineering 2018年第4期31卷 73-83页

作者： Xiao-Dong Jin Yue-Fa Fang Sheng Guo Hai-Bo Qu School of Mechanical Electronic and Control EngineeringBeijing

Most parallel mechanisms(PMs) encountered today have a common disadvantage, i.e., their low rotational *** order to develop PMs with high rotational capability, a family of novel manipulators with one or two dimensional rotations is proposed. The planar one-rotational one-translational(1 R1 T) and one-rotational two-translational(1 R2 T)PMs evolved from the crank-and-rocker mechanism(CRM) are presented by means of Lie group theory. A spatial 2 R1 T PM and a 2 R parallel moving platform with bifurcated large-angle rotations are proposed by orthogonal combination of the RRRR limbs. According to the product principle of the displacement group theory, a hybrid 2 R3 T mechanism in possession of bifurcated motion is obtained by connecting the 2 R parallel moving platform with a parallel part, which is constructed by four 3 T1 R kinematic chains. The presented manipulators possess high rotational capability. The proposed research enriches the family of spatial mechanisms and the construction method provides an instruction to design more complex mechanisms.

关键词： Parallel mechanism Rotational capability Lie group theory Bifurcated motion Hybrid mechanism

Time-inconsistent stochastic linear quadratic control for discrete-time systems

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Science China(Information Sciences) 2017年第12期60卷 44-56页

作者： Qingyuan QI Huanshui ZHANG School of control Science and engineering Shandong University

This paper is mainly concerned with the time-inconsistent stochastic linear quadratic(LQ) control problem in a more general formulation for discrete-time systems. The time-inconsistency arises from three aspects: the coefficient matrices depending on the initial pair, the terminal of the cost function involving the initial pair together with the nonlinear terms of the conditional expectation. The main contributions are: firstly,the maximum principle is derived by using variational methods, which forms a flow of forward and backward stochastic difference equations(FBSDE); secondly, in the case of the system state being one-dimensional, the equilibrium control is obtained by solving the FBSDE with feedback gain based on several nonsymmetric Riccati equations; finally, the necessary and sufficient solvability condition for the time-inconsistent LQ control problem is presented explicitly. The key techniques adopted are the maximum principle and the solution to the FBSDE developed in this paper.

关键词： time-inconsistency open-loop equilibrium control maximum principle FBSDE nonsymmetric Riccati equations

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

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Chinese Physics B 2013年第12期22卷 141-151页

作者：张芳芳刘树堂余卫勇 College of control Science and engineering Shandong University

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.

关键词： modified projective synchronization complex scaling factors complex chaotic systems speed-gradient method

Adaptive Proportional-Derivative Sliding Mode control Law With Improved Transient Performance for Underactuated Overhead Crane Systems

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IEEE/CAA Journal of Automatica Sinica 2018年第3期5卷 683-690页

作者： Menghua Zhang Xin Ma Rui Song Xuewen Rong Guohui Tian Xincheng Tian Yibin Li School of control Science and engineering Shandong University

In this paper, an adaptive proportional-derivative sliding mode control(APD-SMC) law, is proposed for 2D underactuated overhead crane systems. The proposed controller has the advantages of simple structure, easy to implement of PD control, strong robustness of SMC with respect to external disturbances and uncertain system parameters, and adaptation for unknown system dynamics associated with the feedforward parts. In the proposed APD-SMC law, the PD control part is used to stabilize the controlled system, the SMC part is used to compensate the external disturbances and system uncertainties,and the adaptive control part is utilized to estimate the unknown system parameters. The coupling behavior between the trolley movement and the payload swing is enhanced and, therefore, the transient performance of the proposed controller is *** Lyapunov techniques and the La Salle's invariance theorem are employed in to support the theoretical derivations. Experimental results are provided to validate the superior performance of the proposed control law.

关键词： Adaptability adaptive proportional-derivative sliding mode control(APD-SMC) coupling behavior La Salle’s invariance theorem Lyapunov techniques robustness underactuated overhead crane

Optimal control with irregular performance

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Science China(Information Sciences) 2019年第9期62卷 116-129页

作者： Huanshui ZHANG Juanjuan XU School of control Science and engineering Shandong University

In this paper, we solve the long-standing fundamental problem of irregular linear-quadratic（LQ）optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding the analytical solutions to two different forward and backward differential equations（FBDEs）. We give a complete solution to the finite-horizon irregular LQ control problem using a new ‘two-layer optimization' approach. We also obtain the necessary and sufficient condition for the existence of optimal and stabilizing solutions in the infinite-horizon case in terms of solutions to two Riccati equations and the stabilization of one specific system. For the first time, we explore the essential differences between irregular and standard LQ control, making a fundamental contribution to classical LQ control *** show that irregular LQ control is totally different from regular control as the irregular controller must guarantee the terminal state constraint of P1（T）x（T） = 0.

关键词： irregular LQ control Riccati equation stabilization

Global practical tracking via adaptive outputfeedback for uncertain nonlinear systems with generalized control coefficients

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Science China(Information Sciences) 2016年第1期59卷 188-200页

作者： Shaoli JIN Yungang LIU School of control Science and engineering Shandong University

This paper investigates the global practical tracking via adaptive output-feedback for a class of uncertain nonlinear systems with generalized control coefficients. Notably, the system in question has the function-of-output control coefficients and the serious unknowns in the system and the reference signal, and hence is essentially different from the existing closely related literature. To solve the global practical tracking,a high-gain observer is first introduced to reconstruct the unmeasurable system states, and then an adaptive output-feedback controller is designed. It is worth emphasizing that the gains in the designed observer and controller are functions of time and output, for which a novel updating law of the high-gain is introduced to overcome the additional system nonlinearities and the serious unknowns mentioned above. The designed controller is shown such that all the states of the closed-loop system are globally bounded, and furthermore,tracking error will be ultimately prescribed sufficiently small. A numerical simulation is provided to demonstrate the effectiveness of the proposed approach.

关键词： uncertain nonlinear systems function-of-output control coefficients global practical tracking dynamical high-gain adaptive output-feedback

Value iteration algorithm for continuous-time linear quadratic stochastic optimal control problems

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Science China(Information Sciences) 2024年第2期67卷 170-180页

作者： Guangchen WANG Heng ZHANG School of control Science and engineering Shandong University

In this study, we investigate a continuous-time infinite-horizon linear quadratic stochastic optimal control problem with multiplicative noise in control and state variables. Using the techniques of stochastic stability, exact observability, and stochastic approximation, a value iteration algorithm is developed to solve the corresponding generalized algebraic Riccati equation. Unlike the existing policy iteration algorithm, this algorithm does not rely on an initial stabilizing control. Further, this algorithm can also be used to compute policy evaluation steps that arise in the policy iteration algorithm. Herein, a simulation example is provided to validate the obtained results.

关键词： stochastic systems optimal control linear quadratic stochastic problem generalized algebraic Riccati equation value iteration algorithm