A. Ibeas

Stability Results for Switched Linear Systems with Constant Discrete Delays

This paper investigates the stability properties of switched systems possessing several parameterizations (or configurations) while being subject to internal constant point delays. Some of the stability results are formulated based on Gronwalls lemma for global exponential stability, and they are either dependent on or independent of the delay size but they depend on the switching law through the requirement of a minimum residence time. Another set of results concerned with the weaker property of global asymptotic stability is also obtained as being independent of the switching law, but still either dependent on or independent of the delay size, since they are based on the existence of a common Krasovsky-Lyapunov functional for all the above-mentioned configurations. Extensions to a class of polytopic systems and to a class of regular time-varying systems are also discussed.

Stable multi-estimation model for single-input single-output discrete adaptive control systems

A pole-placement-based adaptive controller synthesized from a multi-estimation scheme is designed for linear single-input single-output time-invariant plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterization of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient behaviour while guaranteeing closed loop stability. The scheme becomes specifically useful when extended to linear plants whose parameters are piecewise constants while changing abruptly to new constant parameterizations or in the case when the parameters are slowly time varying rather than constant. Thus, the scheme becomes attractive from a modelling point of view since the plant, while being potentially time varying, or in particular, possessing several operation points, is modelled as a set of time-invariant plant unknown parameterizations each possessing its own estimation scheme. In that way, the model description becomes conceptually simple and easy to implement concerned with both estimation and control issues. A description of the controller architecture with multiple parameterizations, together with its associated multi-estimation scheme is given. In addition, the proofs of boundedness of all the relevant signals are given so that the closed-loop system is proved to be stable.

On the stability properties of linear dynamic time-varying unforced systems involving switches between parameterizations from topologic considerations via graph theory

This paper deals with the stability of linear time-varying systems involving switches through time between different parameterizations of a dynamic linear time-varying system. Graph theory is used to describe the combinations of possible switches of the various sets of parameterizations which ensure the stability of the configurations. Each graph vertex is associated with a particular parameterization while edges (arcs) are associated with switches between the graphs (directed graphs or digraphs). An axiomatic framework is first established concerned with previously known stability results from systems theory related to the achievement of stability when switches between several parameterizations of a dynamic system take place. The axiomatic context is then used to obtain stability results mainly based on the topology of the links between the various configurations associated with a state-trajectory as well as on the nature of the vertices related to the stability of the various isolated parameterizations.

Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control

This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.

A Robustly Stable Multiestimation- Based Adaptive Control Scheme for Robotic Manipulators

A multiestimation-based robust adaptive controller is designed for robotic manipulators. The control scheme is composed of a set of estimation algorithms running in parallel along with a supervisory index proposed with the aim of evaluating the identification performance of each one. Then, a higher-order level supervision algorithm decides in real time the estimator that will parametrize the adaptive controller at each time instant according to the values of the above supervisory indexes. There exists a minimum residence time between switches in such a way that the closed-loop system stability is guaranteed. It is verified through simulations that multiestimation-based schemes can improve the transient response of adaptive systems as well as the closed-loop behavior when a sudden change in the parameters or in the reference input occurs by appropriate switching between the various estimation schemes running in parallel. The closed-loop system is proved to be robustly stable under the influence of uncertainties due to a poor modeling of the robotic manipulator. Finally, the usefulness of the proposed scheme is highlighted by some simulation examples.

ARTIFICIAL INTELLIGENCE AND GRAPH THEORY TOOLS FOR DESCRIBING SWITCHED LINEAR CONTROL SYSTEMS

This paper develops a representation of multi-model based controllers using artificial intelligence techniques. These techniques will be graph theory, neural networks, genetic algorithms, and fuzzy logic. Thus, graph theory is used to describe in a formal and concise way the switching mechanism between the various plant parameterizations of the switched system. Moreover, the interpretation of multi-model controllers in an artificial intelligence frame will allow the application of each specific technique to the design of improved multi-model based controllers. The obtained artificial intelligence-based multi-model controllers are compared with classic single model-based ones. It is shown through simulation examples that a transient response improvement can be achieved by using multi-estimation based techniques. Furthermore, a method for synthesizing multi-model-based neural network controllers from already designed single model-based ones is presented, extending the applicability of this kind of technique to a more general type of controller. Also, some applications of genetic algorithms and fuzzy logic to multi-model controller design are proposed. In particular, the mutation operation from genetic algorithms inspires a robustness test, which consists of a random modification of the estimates which is used to select the one leading to the better identification performance towards parameterizing online the adaptive controller. Such a test is useful for plants operating in a noisy environment. The proposed robustness test improves the selection of the plant model used to parameterize the adaptive controller in comparison to classic multi-model schemes where the controller parameterization choice is basically taken based on the identification accuracy of each model. Moreover, the fuzzy logic approach suggests new ideas to the design of multi-estimation structures, which can be applied to a broad variety of adaptive controllers such as robotic manipulator controller design.

Observer-Based Vaccination Strategy for a True Mass Action SEIR Epidemic Model with Potential Estimation of All the Populations

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among the susceptible and infected. The control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e., susceptible plus infected plus infectious) to asymptotically converge to zero. A state observer is used to estimate the true various partial populations of the susceptible, infected, infectious, and immune which are assumed to be unknown. The model parameters are also assumed to be, in general, unknown. In this case, the parameters are replaced by available estimates to implement the vaccination action.

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

Robust impedance control of robotic manipulators

A task space robust trajectory tracking control is developed for robotic manipulators. A second order linear model, which defines the desired impedance for the robot, is used to generate the reference position, velocity and acceleration trajectories under the influence of an external force. The control objective is to make the robotic manipulators end effector to track the reference trajectories in the task space. A sliding mode based robust control is used to deal with system uncertainties and unmodeled dynamics. Thus, a sliding manifold is defined by a linear combination of the tracking errors of the system in the task space built from the difference between the real and the desired position, velocity and acceleration trajectories. Moreover, the ideal relay has been substituted by a relay with a dead-zone in order to fit in with the actual way in which a real computational device implements the sign function being typical in sliding mode control. Furthermore, a higher level supervision algorithm is proposed in order to reduce the amplitude of the high frequency components of the output associated to an overestimation of the system uncertainties bounds. Then, the robust control law is applied to the case of a robot with parametric uncertainties and unmodeled dynamics. The closed-loop system is proved to be stable while the control objective fulfilled is in practice. Finally, a simulation example which shows the usefulness of the proposed scheme is presented.

Intelligent Control of Discrete Linear Systems Based on a Supervised Adaptive Multiestimation Scheme

A pole-placement based adaptive controller synthesised from a multiestimation scheme is designed for linear plants. A higher level switching structure between the various estimation schemes is used to supervise the reparameterisation of the adaptive controller in real time. The basic usefulness of the proposed scheme is to improve the transient response so that the closed-loop stability is guaranteed. The switching process is subject to a minimum dwelling or residence time within which the supervisor is not allowed to switch between the multiple estimation schemes. The high level supervision is based on the multiestimation identification scheme. The residence time condition guarantees the closed-loop stability. The above higher level switching structure is on-line supervised by a closed-loop tracking error based algorithm. This second supervision on-line tunes the free design parameters which appear as time varying weights in the loss function of the above switching structure. Thus, the closed-loop behaviour, compared to the constant parameter case one, is improved when the design parameter is not tightly initialised. Both supervisors are hierarchically organised in the sense that they act on the system at different rates. Furthermore, a projection algorithm has been considered in the estimation scheme in order to include a possible a priori knowledge of the estimates parameter vector value in the estimation algorithm.