Gong-You Tang

Successive approximation approach of optimal control for nonlinear discrete-time systems

A successive approximation approach designing optimal controller is developed for affine nonlinear discrete-time systems with a quadratic performance index. By using this approach the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law consists of an accurate linear term and a nonlinear compensating term which is the limit of a sequence of adjoint vectors. By taking a finite-time iteration instead of the limit of the sequence of adjoint vectors, we obtain a suboptimal control law. Simulation examples are employed to verify the validity of the proposed algorithm.

Fault diagnosis and fault-tolerant tracking control for discrete-time systems with faults and delays in actuator and measurement

Abstract In this paper, the fault diagnosis (FD) and fault-tolerant tracking control (FTTC) problem for a class of discrete-time systems with faults and delays in actuator and measurement is investigated. In the first step, a discrete delay-free transformation approach is introduced for an constructed augmented system such that the two-point-boundary-value (TPBV) problem with advanced and delayed items can be avoided. Then, the optimal fault-tolerant tracking controller (OFTTC) is proposed with respect to an equivalent reformed quadratic performance index. Moreover, by using the real-time system output rather than the residual errors, a reduced-order-observer-based fault diagnoser for the augmented system is designed to diagnose faults in actuator and measurement, and solve the physically unrealizable problem of proposed OFTTC. Finally, the effectiveness of the proposed fault diagnoser and OFTTC is illustrated by a realistic design example for industrial electric heater.

Optimal tracking control with feedforward compensation for offshore steel jacket platforms with active mass damper mechanisms

This paper presents the optimal tracking control methodology for an offshore steel jacket platform subject to external wave force. Based on a dynamic model of an offshore steel jacket platform with an active mass damper mechanism and a linear exogenous system model of the external wave force on the offshore platform, an optimal tracking control scheme with feedforward compensation is proposed to attenuate the wave-induced vibration of the offshore platform. A feedforward and feedback optimal tracking controller (FFOTC) can be obtained by solving an algebraic Riccati equation and a Sylvester equation, respectively. It is demonstrated that the wave-induced vibration amplitudes of the offshore platform under the FFOTC are much smaller than the ones under the feedback optimal tracking controller (FOTC) and the feedforward and feedback optimal controller (FFOC). Furthermore, the required control force under the FFOTC is smaller than the ones under the FOTC and the FFOC.

Feedforward and feedback optimal control for linear discrete systems with persistent disturbances

Based on the quadratic cost functional index, the optimal control problem of linear discrete-time control systems affected by external persistent disturbances is developed. The main result concerns the existence and design of a realizable, robust feedforward and feedback optimal control law. It is shown that the optimal control law is realizable easily and more robust with respect to additive disturbances than that one of the classical feedback optimal control through simulation.

Sensor Fault and Delay Tolerant Control for Networked Control Systems Subject to External Disturbances

In this paper, the problem of sensor fault and delay tolerant control problem for a class of networked control systems under external disturbances is investigated. More precisely, the dynamic characteristics of the external disturbance and sensor fault are described as the output of exogenous systems first. The original sensor fault and delay tolerant control problem is reformulated as an equivalence problem with designed available system output and reformed performance index. The feedforward and feedback sensor fault tolerant controller (FFSFTC) can be obtained by utilizing the solutions of Riccati matrix equation and Stein matrix equation. Based on the designed fault diagnoser, the proposed FFSFTC is further reconstructed to compensate for the sensor fault and delayed measurement effects. Finally, numerical examples are provided to illustrate the effectiveness of our proposed FFSFTC with different cases with various types of sensor faults, measurement delays and external disturbances.

Approximate design of optimal tracking controller for systems with delayed state and control

Successive approximate design of the optimal tracking controller for linear systems with time-delay is considered. A functional-based transformation is introduced, which transforms the system with control delay into a system without control delay formally. By applying the successive approximation approach of differential equations, the two-point boundary value (TPBV) problem with both time-delay and time-advance terms derived from the original optimal tracking control (OTC) problem is transformed into a sequence of linear TPBV problems without delay and advance terms. By finite iterations of the solution sequence, a suboptimal tracking control law is obtained. The reduced-order reference input observer is constructed to guarantee the feedforward compensator physically realizable. Simulation results demonstrate the effectiveness of the optimal tracking control law.

Optimal tracking control for large-scale interconnected systems with time-delays

This paper considers an infinite-horizon optimal tracking control problem for a class of large-scale interconnected systems with state time-delays. By using the successive approximation approach, two iteration sequences of vector differential equations are constructed. Meanwhile the large-scale interconnected system is decomposed into finite decoupled subsystems. The existence and uniqueness of the optimal solution is proved, as well as the convergence of the solution sequence. By finite iterations of the solution sequence, a suboptimal tracking control law is obtained. A reduced-order reference input observer is designed to make the feedforward term of the optimal tracking control law physically realizable. A numerical example shows that the presented algorithm is effective and easy to implement.

Optimal output tracking control for bilinear systems

We consider the optimal output tracking control (OOTC) problem for a class of bilinear systems with a quadratic performance index. Using a successive approximation approach (SAA), the original non-linear optimal problem is transformed into a sequence of linear non-homogeneous two-point boundary value (TPBV) problems. An adjoint vector sequence can be obtained from the iterative solution of the sequence of TPBV problems. The OOTC law obtained consists of accurate linear feedback and feedforward terms and a non-linear compensation term which is the limit of the adjoint vector sequence. A reference input observer is constructed to make the approximate OOTC law physically realizable. A numerical simulation is provided to illustrate the effectiveness of the proposed method.

Sensitivity approach of optimal control for linear discrete large-scale systems with state time-delay

Based on the sensitivity analysis theory, we proposed an optimal control approach for linear discrete large-scale systems with state time-delay. A sensitivity parameter was introduced to the original two-point boundary problems to eliminate the time-delay and time-advance terms. The problems were further transformed to accelerate the convergence speed. The derived problems have neither time-delay nor time-advance terms. Solving them, we got the optimal control law of the original problems. By intercepting the frontal finite terms of the solution series, we obtained a suboptimal control law.

States observer design and stability analysis for networked control systems

This paper considers the networked control systems whose network-induced delay is likely longer than a sampling period. The continuous time system model with control time-delay is transformed into the discrete time system model with multiple time-delays. Based on the model, a new type full-dimension states observer is designed. A discrete Lyapunov functional method is proposed for the augmented system consisted of the state vector and the error vector to stability analysis. By the method, the asymptotic stability necessary conditions of the augmented system are given. The simulation results show that the method is effective.