Comparison Between Predictive Sliding Mode Control and Sliding Mode Control with Predictive Sliding Function

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

“…Proof: This lemma can be proven by extending the results in Lemma 1: the proof is omitted due to space limitation. Lemma 4: Given system (5) satisfying Assumptions 2-4, consider the nominal evolution ẑt+k ∈ Z and perturbed evolution z t+k ∈ Z, for k ∈ N ≥0 , as defined within Lemma 2 in (20). Recalling the definition of wz in (24), we obtain…”

“…The work in [18] introduces an integral SMC term into an MPC law, to compensate matched disturbances, thus maintaining the state inside a boundary layer of S throughout the entire response; the same idea is extended to unmatched disturbances in [19]. Finally, [20] compares different approaches for combining SMC and MPC.…”

“…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).…”

A predictive sliding mode control for quadrotor’s trackingtrajectory subject to wind gusts and uncertainties

“…The adopted control strategy was based on the dual-mode law that is constructed of twopart: the discrete sliding mode control law where the sliding surface was in the terminal sliding region, and the receding horizon optimization law where the sliding surface was out from the terminal sliding region. A comparative study between DSMC with predictive sliding function (PSF) and predictive sliding mode control is done in [19]. Those strategies are simulated to the linearised isothermal Van de Vussen systems.…”

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

“…In [14], an MPC strategy is proposed for linear and nonlinear systems, which uses the sliding manifold as terminal constraint. Other control schemes, merging an SMC block and an MPC block within an overall feedback scheme, have been proposed in [15]- [18]. Among these, a particularly relevant solution is the use of discrete-time integral SMC, for which analogous results in continuous time are reported in [19], [20].…”