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• In this paper, the finite horizon linear quadratic tracking problem transforms to the finite-horizon linear quadratic regulator problem with the help of the augmented system. • The developed algorithm in this paper solves the time-varying Riccati equations offline and backward-in-time without the system dynamics or any model identification schemes through the defined time-varying Q-function. • Compare with the work in [56], the restrictions on initial state of the developed algorithm in this paper are not required. Besides, optimal tracking control can be achieved in this paper. • Compare with the work in [57], the discrete-time system is studied in this paper. While, continuous-time system is considered in [57]. Besides, there is no restriction on the initial value function of the developed algorithm in this paper, while the initial value function of the developed algorithm in [57] needs to meet certain conditions. Conventionally, the finite-horizon linear quadratic tracking (FHLQT) problem relies on solving the time-varying Riccati equations and the time-varying non-causal difference equations as the system dynamics is known. In this paper, with unknown system dynamics being considered, a Q -function-based model-free method is developed to solve the FHLQT problem. First, an augmented system consisting of the controlled system and the desired trajectory system is formulated, and the FHLQT problem transforms to the finite-horizon linear quadratic regulator (FHLQR) problem with the augmented system. Then, a time-varying Q -function which depends explicitly on the control input is defined. With the defined time-varying Q -function, a model-free finite-horizon control method is developed to approximate the solutions of the time-varying Riccati equations of the transformed FHLQR problem. At last, simulation studies are carried out to verify the validity of the developed method. [ABSTRACT FROM AUTHOR]

• A fast finite-time criterion for deterministic systems is established. • We establish a fast finite-time control criterion for stochastic systems by revamping the fast finite time method. • The control strategy can effectively improve the control speed compared to the existing results in this paper. This paper elucidates the finite-time stability in probability problem for a class of p-norm stochastic nonlinear systems. Among them, from the point of view of convergence speed, finite-time control does have optimal properties. Consequently, a fast finite-time criterion for deterministic systems is established. However, although there exist a significant amount of results on fast finite time stability, there is no article involves p-norm stochastic nonlinear systems case available so far. There are random disturbance terms that made the traditional fast finite-time control methods inapplicable. To overcome this problem, we establish a fast finite-time control criterion for stochastic systems by revamping the fast finite time method of deterministic systems. Then, with the aid of sign function and adding a power integrator technology, a non-Lipschitz continuous state feedback controller is established successfully. Next, the control strategy can effectively improve the control speed compared to the existing results in this paper. Finally, numerical and dynamic suspension simulations are offered to augment our theoretical analysis results, and comparison plots with conventional control strategies are shown. [ABSTRACT FROM AUTHOR]

• An efficient data-driven algorithm is proposed to identify the system dynamics. • The internal model of the exosystem is embedded in the adaptive fault-tolerant law for the first time. • The obtained stability criterion is less conservative than before. In this paper, the adaptive fault-tolerant output regulation for the system with unknown dynamics is considered. Firstly, a data-driven algorithm is proposed to identify the system dynamics by solving the Riccati equation. Due to unneeded to solve the optimal controller, the iterative process of the algorithm is reduced. Based on the identified model, an adaptive controller is designed to compensate for the actuator faults which include both outage and loss-of-effectiveness faults. Moreover, the internal model of the exosystem is embedded in the adaptive fault-tolerant controller which can stabilize the system whether the actuator faults hold or not. Finally, the numerical simulation result shows the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]