Design of nonlinear optimal tracking control law based on finite-time stability for quadratic performance index

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

Three-dimensional suboptimal guidance law based on θ – D technique and nonlinear disturbance observer

In this paper, a nonlinear suboptimal guidance system is presented for the missile targeting an unknown arbitrary target. An integrated quadratic performance index is minimized in this guidance law, and the whole design is based on the exact 3D nonlinear missile-target dynamics without any linearization. Considering that the Hamilton–Jacobi–Bellman equation of a nonlinear system is quite difficult to be solved, the [Formula: see text] method is used to obtain the approximate solution without complicated online computations. Moreover, the target accelerations are regarded as the unknown disturbances, and the robustness against the target maneuvering and the external disturbances is enhanced by introducing the feedforward compensation based on the nonlinear disturbance observer. In addition, no priori knowledge like the time-to-go is needed in this suboptimal guidance law. Simulation studies show that the proposed composite guidance system can guarantee that the missile intercepts the arbitrary maneuvering target with satisfied performance.

Optimal Fault-Tolerant Control against Descriptor Time-Varying Systems with Nonlinear Input

The problem of optimal fault-tolerant control for a class of descriptor time-varying systems with nonlinear input is considered. Based on the Lyapunov stability theorem, the sufficient conditions of the stability are obtained when the system is normal and ineffective. Furthermore, the fault-tolerant control of the systems is carried out in two cases, and the state feedback fault-tolerant controller is obtained to satisfy the quadratic performance index and reach the minimum value in order to achieve the optimal fault-tolerant control. Finally, the validity of the proposed approach is illuminated by a numerical example.

Using Constrained Bilinear Quadratic Regulator for the Optimal Semi-Active Control Problem

Semi-active systems provide an attractive solution for the structural vibration problem. A useful approach, aimed to simplify the control design, is to divide the control system into two parts: an actuator and a controller. The actuator generates a force that tracks a command which is generated by the controller. Such approach reduces the complexity of the control law design as it allows for complex properties of the actuator to be considered separately. In this study, the semi-active control design problem is treated in the framework of optimal control theory by using bilinear representation, a quadratic performance index, and a constraint on the sign of the control signal. The optimal control signal is derived in a feedback form by using Krotov's method. To this end, a novel sequence of Krotov functions which suits the multi-input constrained bilinear-quadratic regulator problem is formulated by means of quadratic form and differential Lyapunov equations. An algorithm is proposed for the optimal control computation. A proof outline for the algorithm convergence is provided. The effectiveness of the suggested method is demonstrated by numerical example. The proposed method is recommended for optimal semi-active feedback design of vibrating plants with multiple semi-active actuators.

Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays

In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the Lyapunov functional for the initial function of time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.

Lyapunov matrices approach to the parametric optimization of a neutral system

In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system. The Lyapunov functional is determined by means of the Lyapunov matrix.