This paper discusses the design of the optimal preview controller for a linear continuous-time stochastic control system in finite-time horizon, using the method of augmented error system. First, an assistant system is introduced for state shifting. Then, in order to overcome the difficulty of the state equation of the stochastic control system being unable to be differentiated because of Brownian motion, the integrator is introduced. Thus, the augmented error system which contains the integrator vector, control input, reference signal, error vector and state of the system is reconstructed. This leads to the tracking problem of the optimal preview control of the linear stochastic control system being transformed into the optimal output tracking problem of the augmented error system. With the method of dynamic programming in the theory of stochastic control, the optimal controller with previewable signals of the augmented error system being equal to the controller of the original system is obtained. Finally, numerical simulations show the effectiveness of the controller.

The problem of static output feedback preview tracking control is proposed for a class of polytopic uncertain discrete‐time systems by combining parameter‐dependent Lyapunov function method with linear matrix inequality (LMI) technique. First, the error system method of preview control theory is adopted and the difference operator is introduced, and then an augmented error system including previewed information is constructed, which transforms a tracking problem into a regulation problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the derived augmented error system while considering the output feedback. Sufficient conditions for designing a robust static feedback preview controller are given in terms of solutions to a set of LMIs. Based on the criterion, a static output feedback controller with preview action is designed such that the output can asymptotically track the reference signal. Finally, the numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the study.

This paper presents the cooperative preview control method for continuous-time multi-agent systems with a time-invariant directed communication topology. First, the cooperative tracking preview control problem is transformed into the optimal regulation problem of an augmented system. Next, by applying the results of the standard optimal preview control of continuous-time linear systems, a controller of the augmented system is obtained. Furthermore, the stabilisability and detectability of the augmented system are studied under the fixed digraph and the prescribed leader. Then, we derive the controller of multi-agent systems with error integral and preview action that can guarantee the achievement of cooperative optimal preview tracking. Finally, the effectiveness of the controller is shown by numerical simulations.

This paper studies the preview control problem of impulse-free linear continuous-time descriptor systems. The system is first decomposed into a normal system (i.e., slow subsystem) and an algebraic equation set, by restricted equivalent linear transformation. Then, applying the method of preview control theory to the slow subsystem, by taking derivatives on both the error vector and the state function, and with the error vector being a part of the new state vector, the augmented system is constructed and the tracking problem is transformed into a regulation problem. According to preview control theory, the controller of the augmented system can be obtained and the control input of the original descriptor system with preview function can be acquired by integrating on the controller of the augmented system. Both the stabilisability and detectability of the augmented system are discussed. Numerical simulation verifies the presented results.