Hierarchical Model Predictive Control of independent systems with joint constraints

A hierarchical MPC scheme for interconnected systems

“…This depends of the fact that, as N L → +∞, both A (N L ) → 0 and B(N L ) → 0. A further remark is that, similarly to Proposition 2.3 in [29], for any i = 1, ..., M it can be proved that lim N L →+∞ λ i (N L ) = +∞, allowing to increase at will the feasibility region of the low-level problem. From the discussion in Section 4.1 it has finally become clear that, by tuning the value of the low-level prediction horizon N L , one can reduce at will the values of ρ δû i , related to the maximum required amplitude of inputs δ u i .…”

“…(3), 3. (4), and more specifically by equations (28) and (29). Importantly, note that the constraints (28) and (29)…”

“…, M, and the reduced order model satisfying Assumption 2 is listed here following the same line as in [29]. Note however that in [29] the case of dynamically decoupled subsystems was considered, and full system reduction actually could be carried out subsystem-by-subsystem. On the contrary, in this case, system reduction must be performed at a full system level and structural additional constraints must be satisfied, i.e.…”

“…Notably, the local regulators can be designed and implemented at different rates to cope with subsystems operating at different time scales, as it often happens in many important industrial fields, see the centralized multirate MPC methods reported in [33,4,23,8,7,22,2], or the multirate implementations described in [32,16,38]. A similar control structure has been already proposed in [29] where however the framework was different: only independent systems Σ i with joint output constraints were considered, no multirate implementations were allowed, and the problem was to coordinate the Σ i s to guarantee an overall output request, so that different technical tools, with respect to the ones here considered, had to be adopted at the two layers of the control structure. The paper is organized as follows.…”

Nonlinear Predictive Sliding Mode Control for Active Suspension System

“…MPC has also been widely involved in the control of nonlinear systems and has achieved good results [10][11][12]. For example, [13][14][15] presented a good solution to nonlinear systems involved in the constrained nonlinear systems through the design of the nonlinear model predictive control (NMPC). Reference [16] designed a robust predictive controller based on the Lyapunov function and solved the problem of constraint and uncertain parameters in the nonlinear system, which guarantees robust performance; [17] developed a NMPC based on Carleman approximation for the nonlinear dynamic constraints.…”