Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection
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ORIGINAL PAPER
Command filtered robust control of nonlinear systems with full-state time-varying constraints and disturbances rejection Guichao Yang
. Hua Wang . Jie Chen . Hao Zhang
Received: 1 October 2019 / Accepted: 25 August 2020 Springer Nature B.V. 2020
Abstract For the barrier Lyapunov function-based control of full-state time-varying constrained systems via the traditional backstepping technology, due to repeated differentiations of virtual control functions involving time-varying barriers, the adverse effects of ‘‘explosion of complexity’’ caused by the backstepping iteration are more serious, which even makes it impossible to implement for high-order systems. In order to eliminate this negative influence, we take advantage of the command filtered backstepping approach which introduces a command filter to approximate the constructed virtual control law in each procedure of the backstepping design. More importantly, the approximate errors arising from the introduced filters will be removed by constructing a series of compensating signals. Meanwhile, some relatively conservative assumptions will be released compared with existing control strategies. Furthermore, largely unknown external disturbances that may exist in the system will be estimated in real-time via high-gain disturbance observers and then compensated feedforwardly in designing the controller. Specially, the scheme of the resulting control algorithm is simple and online computation time is saved. Finally, G. Yang H. Wang (&) J. Chen H. Zhang School of Mechanical and Power Engineering, Nanjing Tech University, Nanjing 211816, China e-mail: [email protected] G. Yang e-mail: [email protected]
the stability of the whole closed-loop system and the control performance is strictly certificated, respectively. Keywords Nonlinear systems Full-state timevarying constraints Robust control Command filtered backstepping Barrier Lyapunov function Disturbances rejection
1 Introduction For practical systems, they often suffer from constraints in the form of saturation, physical stoppages, performance specifications, safety restrictions, and so on [1]. Currently, developing advanced control strategies to deal with constraints has become one of the significant research topics. The existing constrainthandling algorithms mainly include the exploitation of set invariance notions [2], model predictive control (MPC) [3, 4], reference governors [5], Barrier Lyapunov Function (BLF)-based control schemes [1, 6–11], and so on. In general, control methods on basis of BLF as powerful means to deal with constraints have been the most common during the last decade. Furthermore, with the development of control theory, the current control for constraints mainly goes through a process from single output constraints to more comprehensive state–state
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constraints. Moreover, due to the more general significance of time-varying constraints control, it has also experienced the de
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