Discrete predictive sliding mode control of uncertain systems

Constrained Nonlinear Discrete-Time Sliding Mode Control Based on a Receding Horizon Approach

“…Apart from the listed technical challenges, the main contribution of this work consists of defining a DSMC law for uncertain and possibly multi-input nonlinear systems, directly based on the nonlinear dynamics, that guarantees the satisfaction of both input and state constraints in a general form. Such a result, to the best of our knowledge, is not available in the literature, as the cited papers either deal with linear systems [8], [10], [11], [13]- [15] or linear systems approximations [9], or generate an overall control law that is not a DSMC law [12], or finally use a DSMC controller to enhance the robustness properties of a separate MPC controller [16]- [20]. Notice that, when the state constraints are defined directly on the components of the sliding variable, one could design a sliding mode controller without the need for receding-horizon approaches, so as to force the state to slide on the boundary of the admissible region (i.e., the region of the state space in which all state constraints are satisfied), whenever this boundary is reached, thus satisfying the imposed constraints (see, e.g., [24] for continuous-time SMC).…”

“…The same approach was extended to nonlinear systems, but relying on a linear approximation of the dynamics [9]. As an alternative, in [10], the DSMC reaching law of [3] generates a reference for an MPC controller, for the case of unconstrained single-input uncertain linear systems. Also, [11] proposes an MPC law for single-input perturbed linear systems, which guarantees asymptotic convergence of the state to a boundary layer of S. Moreover, [12] presents single-input MPC laws for unperturbed linear and nonlinear systems, where S is used to define the terminal constraint of the MPC problem, while [13] proposes a DSMC law for linear multi-input systems based on the solution of a robust linear MPC problem: the resulting control law guarantees finite-time convergence of the state onto S (in case of vanishing disturbance) or into an apriori determined boundary layer of it (in case of persistent disturbance).…”

Quasi-SMC based on MPC for a constrained continuous-time nonlinear system with external disturbances

“…The other type is to merge SMC and MPC into a single control law. In [19], [20], considering an unconstrained linear system, MPC controller generates the control law based on SMC reaching law to improve the performance of SMC. The linear system with constraints is further considered in [21], [22], which guarantee the convergence of state to the sliding mode band.…”

A Discrete-Time Optimization-Based Sliding Mode Control Law for Linear Systems with Input and State Constraints

“…Earlier works consider the possibility of merging DSMC and generalized predictive control to obtain explicit control laws for linear systems [10], [11]. In [12], the reaching law defined in [6] is used to define a sliding mode trajectory reference for an MPC controller. In [13], an MPC law is formulated for linear systems, by defining the MPC cost function as the distance of the state from the sliding manifold, which leads to the guarantee of asymptotic convergence of the sliding variable to a PSMB.…”