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

Congestion management in traffic-light intersections via Infinitesimal Perturbation Analysis

We present a flow-control technique in traffic-light intersections, aiming at regulating queue lengths to given reference setpoints. The technique is based on multivariable integrators with adaptive gains, computed at each control cycle by assessing the IPA gradients of the plant functions. Moreover, the IPA gradients are computable on-line despite the absence of detailed models of the traffic flows. The technique is applied to a two-intersection system where it exhibits robustness with respect to modeling uncertainties and computing errors, thereby permitting us to simplify the on-line computations perhaps at the expense of accuracy while achieving the desired tracking. We compare, by simulation, the performance of a centralized, joint two-intersection control with distributed control of each intersection separately, and show similar performance of the two control schemes for a range of parameters

Distributed Robust Consensus Control of Multi-agent Systems with Heterogeneous Matching Uncertainties

This paper considers the distributed consensus problem of linear multi-agent systems subject to different matching uncertainties for both the cases without and with a leader of bounded unknown control input. Due to the existence of nonidentical uncertainties, the multi-agent systems discussed in this paper are essentially heterogeneous. For the case where the communication graph is undirected and connected, a distributed continuous static consensus protocol based on the relative state information is first designed, under which the consensus error is uniformly ultimately bounded and exponentially converges to a small adjustable residual set. A fully distributed adaptive consensus protocol is then designed, which, contrary to the static protocol, relies on neither the eigenvalues of the Laplacian matrix nor the upper bounds of the uncertainties. For the case where there exists a leader whose control input is unknown and bounded, distributed static and adaptive consensus protocols are proposed to ensure the boundedness of the consensus error. It is also shown that the proposed protocols can be redesigned so as to ensure the boundedness of the consensus error in the presence of bounded external disturbances which do not satisfy the matching condition. A sufficient condition for the existence of the proposed protocols is that each agent is stabilizable.Comment: 16 page, 10 figures. This manuscript is an extended version of our paper accepted for publication by Automatic

Synthesis and control of generalised dynamically substructured systems

The experimental technique for testing engineering systems via the method of dynamic substructuring is receiving significant global interest, for example in the fields of large-scale structural, aerospace, and automotive system testing. Dynamically substructured systems (DSSs) enable full-size, critical components of a complete system to be physically tested in real-time, within a laboratory environment, while the remainder of the system is modelled numerically. The intention is that the combined physical-numerical DSS behaves as if it were the complete (or emulated) system.In an ideal mechanical DSS, for example, perfect synchronization of displacements and forces at the interfaces between the numerical and physical components (or substructures) is required. Hence, a key design feature of successful DSS systems is the high fidelity of the control action. Equally, a DSS controller must be able to cope with non-linear, time-varying, and uncertain parameters within the physical substructure dynamics.The main purpose of this paper is to present a generalized DSS framework, together with associated linear and adaptive control strategies, that are specifically tailored to achieve high synchronization performance. The initial studies of this problem, as described in an earlier paper by Stoten and Hyde, are therefore continued by generalizing both the DSS dynamics and the control strategies to include (a) a number of newly defined modes of operation and (b) multivariable dynamics. In addition, comparative implementation and simulation studies are included, based upon the DSS testing of a mechanical system (a planar quasi-motorcycle rig), which was specifically designed to highlight the main features of this research. The comparative studies show that excellent DSS control can be achieved, especially with the addition of an adaptive component to the controller, despite significant changes to the physical substructure dynamics

An adaptive tracking observer for failure-detection systems

The design problem of adaptive observers applied to linear, constant and variable parameters, multi-input, multi-output systems, is considered. It is shown that, in order to keep the observer's (or Kalman filter) false-alarm rate (FAR) under a certain specified value, it is necessary to have an acceptable proper matching between the observer (or KF) model and the system parameters. An adaptive observer algorithm is introduced in order to maintain desired system-observer model matching, despite initial mismatching and/or system parameter variations. Only a properly designed adaptive observer is able to detect abrupt changes in the system (actuator, sensor failures, etc.) with adequate reliability and FAR. Conditions for convergence for the adaptive process were obtained, leading to a simple adaptive law (algorithm) with the possibility of an a priori choice of fixed adaptive gains. Simulation results show good tracking performance with small observer output errors and accurate and fast parameter identification, in both deterministic and stochastic cases

A MRAS-based Learning Feed-forward Controller

Inspired by learning feed–forward control structures, this paper considers the adaptation of the parameters of a model–reference based learning feed–forward controller that realizes an inverse model of the process. The actual process response is determined by a setpoint generator. For linear systems it can be proved that the controlled system is asymptotically stable in the sense of Liapunov. Compared with more standard model reference configurations this system has a superior performance. It is fast, robust and relatively insensitive for noisy measurements. Simulations with an arbitrary second–order process and with a model of a typical fourth–ordermechatronics process demonstrate this