Robust and Resilient State-dependent Control of Continuous-time Nonlinear Systems with General Performance Criteria

A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system

Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

A novel state dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum

A method for computing quadratic Brunovsky forms

In this paper, for continuous, linearly-controllable quadratic control systems with a single input, an explicit, constructive method is proposed for studying their Brunovsky forms, initially studied in [W. Kang and A. J. Krener, Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems, SIAM Journal on Control and Optimization, 30:1319-1337, 1992]. In this approach, the computation of Brunovsky forms and transformation matrices and the proof of their existence and uniqueness are carried out simultaneously. In addition, it is shown that quadratic transformations in the aforementioned paper can be simplified to prevent multiplicity in Brunovsky forms. This method is extended for studying discrete quadratic systems. Finally, computation algorithms for both continuous and discrete systems are summarized, and examples demonstrated.Comment: Author's name was listed as Wenlong Ji

Coupled State-Dependent Riccati Equation Control for Continuous Time Nonlinear Mechatronics Systems

This manuscript considers the coupled state-dependent Riccati equation approach for systematically designing nonlinear quadratic regulator and H ∞ control of mechatronics systems. The state-dependent feedback control solutions can be obtained by solving a pair of coupled state-dependent Riccati equations, guaranteeing nonlinear quadratic optimality with inherent stability property in combination with robust ℓ 2 type of disturbance reduction. The derivation of this control strategy is based on Nash\u27s game theory. Both of finite and infinite horizon control problems are discussed. An underactuated robotic system, Furuta rotary pendulum, is used to examine the effectiveness and robustness of this novel nonlinear control approach

Guaranteed robustness properties of multivariable, nonlinear, stochastic optimal regulators

The robustness of optimal regulators for nonlinear, deterministic and stochastic, multi-input dynamical systems is studied under the assumption that all state variables can be measured. It is shown that, under mild assumptions, such nonlinear regulators have a guaranteed infinite gain margin; moreover, they have a guaranteed 50 percent gain reduction margin and a 60 degree phase margin, in each feedback channel, provided that the system is linear in the control and the penalty to the control is quadratic, thus extending the well-known properties of LQ regulators to nonlinear optimal designs. These results are also valid for infinite horizon, average cost, stochastic optimal control problems

Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

A new separation result for Euler-Lagrange-like systems

This paper presents a separation result for some global stabilization via output feedback of a class of quadratic-like nonlinear systems, under the form of some stabilizability by state feedback on the one hand, and unboundedness observability on the other hand. They allow to design, for any domain of output initial condition, a dynamic output feedback controller achieving global stability. As an example, these conditions are shown to be satisfied by so-called Euler-Lagrange systems, for which a tracking output feedback control law is thus proposed