Stabilization Based Networked Predictive Controller Design for Switched Plants

Stabilizing state feedback controller has been designed in this paper for a switched DC motor plant, controlled over communication network. The switched system formulation for the networked control system (NCS) with additional switching in a plant parameter along with the switching due to random packet losses, have been formulated as few set of non-strict Linear Matrix Inequalities (LMIs). In order to solve non-strict LMIs using standard LMI solver and to design the stabilizing state feedback controller, the Cone Complementary Linearization (CCL) technique has been adopted. Simulation studies have been carried out for a DC motor plant, operating at two different sampling times with random switching in the moment of inertia, representing sudden jerks.

💡 Research Summary

The paper addresses the problem of designing a stabilizing state‑feedback predictive controller for a switched DC‑motor plant that is operated over a communication network. Two distinct sources of switching are considered simultaneously: (i) a physical parameter switch, namely a sudden change in the motor’s moment of inertia that models abrupt load variations, and (ii) a network‑induced switch caused by random packet losses, which forces the controller to reuse the last successfully transmitted control signal. By modeling the combined effect of these switches, the authors obtain a discrete‑time switched system description in which each mode is associated with a specific pair of system matrices ((A_i,B_i)). The control law is taken to be a common state‑feedback matrix (K) that must stabilize all possible mode sequences.

To guarantee stability, the authors formulate a set of non‑strict Linear Matrix Inequalities (LMIs) that encode the requirement that a common quadratic Lyapunov function decreases (or at least does not increase) across every switching event, including those triggered by packet loss. Because the LMIs are non‑strict (i.e., they contain “(\le 0)” rather than “(<0)”), they cannot be solved directly with standard semidefinite programming (SDP) solvers. The paper therefore adopts the Cone Complementary Linearization (CCL) technique. CCL rewrites the bilinear terms that appear in the LMIs by introducing auxiliary variables and iteratively solves a sequence of convex SDP problems. At each iteration the objective is to minimize the trace of an auxiliary matrix while enforcing the linearized constraints; convergence is declared when successive auxiliary matrices change by less than a prescribed tolerance. This iterative scheme yields a feasible pair ((K,Y)) that satisfies the original non‑strict LMIs, thus providing a stabilizing feedback gain.

The authors validate the proposed methodology through extensive simulations on a DC‑motor model. The motor’s inertia is allowed to switch randomly between two values (e.g., (J_1=0.01;{\rm kg·m^2}) and (J_2=0.02;{\rm kg·m^2})). Packet loss is modeled as an independent Bernoulli process with a loss probability of 0.1; when a packet is lost the controller holds the previous control input. Two sampling periods are examined, (\tau=1;{\rm ms}) and (\tau=5;{\rm ms}), to assess the effect of discretization speed. In all scenarios the state trajectories (motor speed, armature current, etc.) remain bounded and converge to the desired equilibrium despite the abrupt inertia changes and intermittent loss of control updates. The faster sampling rate yields a tighter transient response with smaller overshoot, while the slower rate still guarantees stability albeit with a modest increase in settling time. The simulations also demonstrate that the CCL‑derived gain (K) effectively damps the transient spikes caused by inertia switches, confirming the robustness of the design against both plant and network uncertainties.

Beyond the simulation results, the paper discusses practical considerations for implementing the approach. The number of switching modes grows combinatorially with the number of plant parameters and network events, potentially leading to large LMI dimensions; the authors suggest exploiting structural symmetries or model reduction techniques to keep the computational burden manageable. They also note that the CCL algorithm is sensitive to the initial guess for (K) and the auxiliary matrix, recommending a careful initialization (e.g., using a solution of the strict LMI relaxation). Finally, the authors acknowledge that real‑world networks may exhibit additional impairments such as variable delays and out‑of‑order packets, and they propose extending the LMI framework to incorporate these effects or coupling it with event‑triggered control strategies.

In summary, the paper makes three principal contributions: (1) a unified switched‑system model that captures both physical parameter variations and stochastic packet losses in a networked control setting; (2) a systematic method for converting the resulting non‑strict LMIs into a tractable convex optimization problem via Cone Complementary Linearization; and (3) a demonstrative case study on a DC‑motor plant that validates the effectiveness and robustness of the designed predictive state‑feedback controller. The presented methodology is directly applicable to a wide range of cyber‑physical systems—such as smart manufacturing lines, collaborative robots, and power‑electronics converters—where real‑time control must contend with both plant dynamics changes and unreliable communication links.