Design of nonlinear optimal tracking control law based on finite-time stability for quadratic performance index

In this paper, a design method of optimal tracking control based on finite-time stability for quadratic performance index is proposed. Finite-time stability of tracking control involves dynamical systems whose actual output can track desired output in finite time while satisfying Lyapunov stability. A nonlinear control law which guaranteed finite-time stability is designed depending on the core idea of dynamic programming. By using Hamilton–Jacobi–Bellman (HJB) equation and finite-time stability theory, sufficient conditions involving V-function are provided, and design steps for nonlinear finite-time tracking control law are derived by constructing augmented systems. In addition, the V-function is constructed to obtain corresponding law for given systems, which verified that the design method is feasible. Simulation examples validate the efficiency of the results.

Dynamic modelling and linear quadratic sliding mode control of a multivariable looper system in hot strip mills

This paper introduces a linear quadratic sliding mode control (LQ-SMC) scheme into a looper control system. First, according to a 1700 mm tandem hot mill, the state-space dynamic model of the looper system was established, and then, the optimal control law of the looper system was obtained based on the established model. Finally, the optimal sliding mode and optimal sliding mode control law of the LQ-SMC scheme were designed such that the sliding motion could satisfy the optimal value of the quadratic performance index. Simulation results show that the proposed control scheme has complete robustness to external disturbances that satisfies certain conditions, and the coupling between the looper angle dynamic and strip tension dynamic is also minimized.

Transforming linear time-varying optimal control problems with quadratic criteria into quadratic programming ones via wavelets

In this paper, an algorithm for solving optimal control of linear time-varying systems with quadratic performance indices is presented. By using important matrices which are derived from Chebyshev wavelets properties, the original problem is converted to a quadratic programming one. This parameter optimization method is applied on both constrained and unconstrained control systems having linear state equations of integer and fractional orders. The computing time saved by this approach is much better than with other methods in which there is no need to calculate the optimal costs of systems by substituting the approximations of the state and control vectors and their values are default outputs of the quadprog solvers.

The archived-based genetic programming for optimal design of linear/non-linear controllers

Evaluation of control signal function is one of the critical subjects in the optimal control problems. The optimal control is usually obtained by optimizing a performance index that is a weighted combination of control effort and state trajectories in the quadratic form, typically known as quadratic performance index (QPI). For the simple case of linear time-invariant (LTI) systems, problems are commonly solved using the well-established governing Riccati equation; however, obtaining the analytical solutions for linear time-variant (LTV) and nonlinear systems has always been highly debated in the optimal control problems. In this study, a newly developed type of Genetic Programming called the archived-based genetic programming (AGP) is presented. Using this algorithm, the analytical solutions for any type of optimal control problems can be obtained faster and more efficiently than the ordinary GPs. Subsequently, due to the inefficiency of QPI in capturing the general behavior of signals, a new performance index named the absolute performance index (API) is proposed in this study. Since the developed AGP algorithm could find the analytical solutions irrespective of the conventional mathematical calculations, it can be effectively implemented to solve the introduced API measures. According to the analytical results, it is observed that in a given problem, the solutions of API are more compatible with the design goals compared with QPI. Furthermore, it is shown that some new forms of the control signals such as impulse solutions, which may not be obtained using QPI, can only be estimated using API in defining the optimal control problems.