Dinh Hoa Nguyen

A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min-max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min-max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min-max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.

Hierarchical Decentralized Stabilization for Networked Dynamical Systems by LQR Selective Pole Shift

Abstract This paper proposes a systematic method to design hierarchical, decentralized, stabilizing controllers for homogeneous hierarchical dynamical networks. Based on LQR approach with a properly chosen performance index including global and local objectives with control input penalty, an obtained optimal LQR feedback gain gives the closed-loop system a prescribed desirable hierarchical structure. In addition, the undesirable eigenvalues of the given homogeneous network can be selectively shifted by further selecting the weighting matrices based on the left eigenvectors associated with those eigenvalues. Finally, the proposed method is summarized into a systematic design procedure with an illustrative numerical example to show its effectiveness.

An interpolation method of multiple terminal iterative learning control

In this paper, we present an iterative learning control (ILC) algorithm to track specified desired multiple terminal points at given time instants. A framework to update the desired trajectories from given points is developed based on the interpolation technique. The approach shows better rate of convergence of the errors. The simulation with a satellite antenna control model is demonstrated to show the effectiveness of our approach.

Iterative learning control for optimal multiple-point tracking

This paper presents a new optimization-based iterative learning control (ILC) framework for multiple-point tracking control. Conventionally, one demand prior to designing ILC algorithms for such problems is to build a reference trajectory that passes through all given points at given times. In this paper, we produce output curves that pass close to the desired points without considering the reference trajectory. Here, the control signals are generated by solving an optimal ILC problem with respect to the points. As such, the whole process becomes simpler; key advantages include significantly decreasing the computational cost and improving performance. Our work is then examined in both continuous and discrete systems.

Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties

This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min–max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min–max problem. By finding an upper bound of the worst-case performance, the min–max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.