Control Problem For Time-delay Systems Research Articles

A Value Iteration Approach to Adaptive Optimal Control of Linear Time-Delay Systems

This paper studies the adaptive optimal control for linear time-delay systems described by delay differential equations (DDEs). A key strategy is to exploit the value iteration (VI) approach to solve the linear quadratic optimal control problem for time-delay systems. However, previous learning-based control methods are all exclusively devoted to discrete-time time-delay systems. In this article, we aim to fill in the gap by developing a learning-based VI approach to solve the infinite-dimensional algebraic Riccati equation (ARE) for continuous-time time-delay systems. One nice feature of the proposed VI approach is that an initial admissible controller is not required to start the algorithm. The efficacy of the proposed methodology is demonstrated by the example of autonomous driving.

Robust Control for a Class of Time-delay Nonlinear Systems via Output Feedback Strategy

This paper studies the robust control problem for time-delay systems with complicated inherent nonlinearities and unknown disturbances. Based on the modified homogeneous domination method and by constructing the proper Lyapunov-Krasovskii (L-K) functional, output feedback controllers are successfully constructed to guarantee the boundedness of all the states of the closed-loop system. The convergence of the states is also realizable when the L2 norm of the disturbance exists. The presented method is also extended to solve the control problem of nonholonomic time-delay system. Simulation examples are given to show the effectiveness of the proposed theory.

Adaptive-gain observer-based control of a class of time-delay systems subject to output-slope non-linearities

A non-linear adaptive observer is proposed to estimate the unmeasured states of a class of time-delay non-linear systems. Irrespective of the size of the constant delay, it is shown that the observer is globally convergent if the growth rate of the system non-linearities is output dependent. The presented results generalize previous results on observation of Lipschitz time-delay systems. Subsequently, the observerbased control problem of time-delay systems, having triangular structure, is discussed for arbitrary large constant delay.

A Walsh series approach to time-delay control system observer design

The optimal control problem of time-delay systems with partial state measurements is studied through the application of a, Walsh function expansion. The main purpose of the paper is to provide a computational technique for determining the expansion coefficient matrices for both the system state and the observer output. It is shown that the known initial conditions of the state and the observer can be used iteratively to compute the state and the observer at any subsequent time and thus implement the optimal controller. Also, by subdividing the time interval of interest, the procedure is simplified such that it does not involve any matrix inversion.