This paper proposes a necessary and sufficient condition of convergence in the L₂-norm sense for a feedback-based iterative learning control (ILC) system including a multi-input multi-output (MIMO) linear time-invariant (LTI) plant. It is shown that the convergence conditions for a nominal plant and an uncertain plant are equal to the nominal performance condition and the robust performance condition in the feedback control theory, respectively. Moreover, no additional effort is required to design an iterative learning controller because the performance weighting matrix is used as an iterative learning controller. By proving that the least upper bound of the L₂-norm of the remaining tracking error is less than that of the initial tracking error, this paper shows that the iterative learning controller combined with the feedback controller is more effective to reduce the tracking error than only the feedback controller. The validity of the proposed method is verified through computer simulations.

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Feedback-Based Iterative Learning Control for MIMO LTI Systems

In distributed mobile robot systems, autonomous robots accomplish complicated tasks through intelligent cooperation with each other. This paper presents behavior learning and online distributed evolution for cooperative behavior of a group of autonomous robots. Learning and evolution capabilities are essential for a group of autonomous robots to adapt to unstructured environments. Behavior learning finds an optimal state-action mapping of a robot for a given operating condition. In behavior learning, a Q-learning algorithm is modified to handle delayed rewards in the distributed robot systems. A group of robots implements cooperative behaviors through communication with other robots. Individual robots improve the state-action mapping through online evolution with the crossover operator based on the Q-values and their update frequencies. A cooperative material search problem demonstrated the effectiveness of the proposed behavior learning and online distributed evolution method for implementing cooperative behavior of a group of autonomous mobile robots.

/pdf/online-evolution-for-cooperative-behavior-in-group-robot-40loof8uhs.pdf

Online Evolution for Cooperative Behavior in Group Robot Systems

An improved linear matrix inequality (LMI) representation of delay-independent H₂ performance analysis is introduced for linear delay systems with delays of any size. Based on this representation we propose a new H₂ memoryless state feedback design. By introducin g a new matrix variable, the new LMI formulation enables us to parameterize memoryles s controllers without involving the Lyapunov variables in the formulations. By using a parameter-dependent Lyapunov function, this new representation proposed here provides us the results with less conservatism.

/pdf/improved-delay-independent-h-performance-analysis-and-3nhlfml4pa.pdf

Improved Delay-independent H₂ Performance Analysis and Memoryless State Feedback for Linear Delay Systems with Poly topic Uncertainties

Solution bounds for algebraic equations in control theory

In the extension to multi-input nonlinear uncertain systems of the sliding mode methodology, a crucial role is played by the matrix pre-multiplying the control in the dynamic equation of the sliding output. If this matrix is perfectly known and invertible, it is possible to transform a multi-input sliding mode control problem in an almost decoupled set of single-input problems. If this matrix is uncertain then nothing can be done in general, and the investigation is oriented to find conditions ensuring the feasibility of control strategies in a progressively more general set of uncertain matrices. In the case of uncertain and constant matrices, it is possible, in principle, to manage the case in which the matrix in question is invertible. The corresponding adaptive or switching strategy suffers from the curse of dimensionality of the so-called unmixing set. In this article the case of time- and state-varying uncertain matrix is dealt with. A more general class of such a matrices for which there is, at lea...

/pdf/multi-input-sliding-mode-control-of-nonlinear-uncertain-559s3ce83c.pdf

Multi-input sliding mode control of nonlinear uncertain affine systems

A new result for bounding the summations for solution eigenvalues of the algebraic Lyapunov equation is presented. This makes possible to generate the best known upper scalar solution estimates.

New upper estimates for the solution of the continuous algebraic Lyapunov equation

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

/pdf/new-upper-bounds-for-the-cale-a-singular-value-decomposition-3roxty8pgo.pdf

New Upper Bounds for the CALE : A Singular Value Decomposition Approach

A new upper trace bound, which generalizes the best available similar estimates, improves their tightness and holds under a less conservative validity restriction imposed on the coefficient matrix, is derived for the solution matrix of the continuous algebraic Lyapunov equation (CALE). Two numerical examples illustrate the applicability of the main result.

/pdf/new-generalized-upper-trace-bound-for-the-solution-of-the-5byorr7jtt.pdf

New generalized upper trace bound for the solution of the lyapunov equation

The improvement problem for available lower and upper trace bounds for the solution of the continuous-time Lyapunov equation (LE) is investigated. It is shown how an arbitrary positive (semi)-definite lower matrix solution bound can be used to get always tighter trace estimates.

http://doi.baspress.com/pdf-journal/Comptes%20Rendus_5_2013/5_2013_16.pdf

Svetoslav Savov

Papers

New upper estimates for the solution of the continuous algebraic Lyapunov equation

New Upper Bounds for the CALE : A Singular Value Decomposition Approach

New generalized upper trace bound for the solution of the lyapunov equation

Noniterative Improvement of Trace Bounds for the Lyapunov Equation Solution

The continuous algebraic Lyapunov's equation. Lower and upper matrix bounds