Synthetic Lyapunov stabilization technique for designing actuation-constrained multi-input multi-output control systems

Abstract

The main objective of this paper is to present a non-predictive method in the design of nonlinear multi-input multi-output (MIMO) control systems with the presence of constraints that are determinant in practical conditions, namely, the frequency bandwidth limitation of the actuation system and saturation boundaries in control commands. If these constraints are applied in the non-predictive control design problem, it is not possible to simultaneously satisfy Lyapunov stability and actuation constraints, analytically. Instead of model-predictive-based algorithms, which in most cases are computationally expensive, this paper proposes an algorithm based on synthetic Lyapunov stability. In this technique, by defining an intelligent filter applied to the system desired trajectories, defining intelligent proximity coefficients in decoupled inequalities resulting from Lyapunov stability, and determining the admissible boundaries of control commands, a space of regulatory parameters is generated. By appropriately adjusting these parameters based on statistical analysis conducted on the overall dynamics of the system, the Lyapunov stability is guaranteed, and the mentioned control constraints are not violated. In summary, the proposed control algorithm includes the formulation of discrete-time dynamics of sliding functions, the presentation of the procedure of defining and adjusting the control algorithm parameters with the proposed synthetic stability criterion, and the calculation of control inputs based on constraints imposed on the problem. Finally, the algorithm is applied to a cart moving in the X-Y plane, including two rigid cooperative arms that are carrying a load. The most important features of synthetic Lyapunov stability compared to the model predictive-based method are its small computational load and its acceptable performance in satisfying both the Lyapunov stability conditions and determinant control constraints in more realistic situations.