Discrete-time integral MRAC with minimal controller synthesis and parameter projection

Model reference adaptive controllers with Minimal Control Synthesis are effective control algorithms to guarantee asymptotic convergence of the tracking error to zero not only for disturbance-free uncertain linear systems, but also for highly nonlinear plants with unknown parameters, unmodeled dynamics and subject to perturbations. However, an apparent drift in adaptive gains may occasionally arise, which can eventually lead to closed-loop instability. In this paper, we address this key issue for discrete-time systems under L-2 disturbances using a parameter projection algorithm. A consistent proof of stability of all the closed-loop signals is provided, while tracking error is shown to asymptotically converge to zero. We also show the applicability of the adaptive algorithm for digitally controlled continuous-time plants. The proposed algorithm is numerically validated taking into account a discrete-time LTI system subject to parameter uncertainty, parameter variations and L-2 disturbances. Finally, as a possible engineering application of this novel adaptive strategy, the control of a highly nonlinear electromechanical actuator is considered. (C) 2015 The Franldin Institute. Published by Elsevier Ltd. All rights reserved.Postprint (author's final draft

Convergence and frequency-domain analysis of a discrete first-order model reference adaptive controller

SUMMARY We study the convergence properties of a direct model reference adaptive control system by applying techniques from numerical analysis. In particular, a first-order discrete system coupled to a minimal control synthesis algorithm discretized by the one-step one-stage zero-order-hold sampling is studied. This results in a strongly non-linear dynamic system owing to the adaptive mechanism where stability at steady state, i.e. at the operating point, equates to successful control. This paper focuses on the convergence analysis of the overall dynamical system for understanding accuracy, stability and performance at steadystate. The local stability of the steady state solution is considered by linearizing the system in the neighbourhood of an operating point when the input is a step function. This analysis allows us to specify two gain space domains which define the region of local stability. Moreover, both the accuracy and the frequency-domain analyses give insight into the range of adaptive control weightings that results in optimal performance of the minimal control synthesis algorithm and also highlights a possible approach to a priori selection of the time step and adaptive weighting values. The effectiveness of the proposed analysis is further demonstrated by simulations and experiments on a first-order plant. Copyright # 2006 John Wiley & Sons, Ltd

Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft

StocHy: automated verification and synthesis of stochastic processes

StocHy is a software tool for the quantitative analysis of discrete-time stochastic hybrid systems (SHS). StocHy accepts a high-level description of stochastic models and constructs an equivalent SHS model. The tool allows to (i) simulate the SHS evolution over a given time horizon; and to automatically construct formal abstractions of the SHS. Abstractions are then employed for (ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy allows for modular modelling, and has separate simulation, verification and synthesis engines, which are implemented as independent libraries. This allows for libraries to be easily used and for extensions to be easily built. The tool is implemented in C++ and employs manipulations based on vector calculus, the use of sparse matrices, the symbolic construction of probabilistic kernels, and multi-threading. Experiments show StocHy's markedly improved performance when compared to existing abstraction-based approaches: in particular, StocHy beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions). StocHy is available at www.gitlab.com/natchi92/StocHy

Advanced theoretical and experimental studies in automatic control and information systems

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included