Showing papers by "Francesco Amato published in 2014"

Input-output finite-time stabilisation of linear systems with input constraints

Abstract: In this study, the problem of input–output finite-time stabilisation of linear time-varying systems is dealt with. The classical definition of input-output finite-time stability (IO-FTS) is extended to that one of structured IO-FTS, which allows to incorporate, in the definition of the stabilisation problem, some amplitude constraints on the control input variables. A sufficient condition and a necessary and sufficient condition for structured IO finite-time stabilisation are provided in the case of L ∞ and L 2 inputs, respectively. Such conditions require the existence of a solution to a certain differential linear matrix inequality. The theory is applied to design the active suspension control system for a two-degree-of-freedom quarter-car model.

Guaranteed cost control for uncertain nonlinear quadratic systems

Abstract: The problem of the robust and optimal control for uncertain quadratic systems is dealt with in this paper. Resorting to a guaranteed cost approach, this paper proposes a novel control design methodology which enables to find a state feedback controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point; iii) the satisfaction of a quadratic performance index. The control performance is guaranteed against parametric uncertainties which are assumed to be norm-bounded. This design procedure involves the solution of a Linear Matrix Inequalities (LMIs) optimization problem, which can be efficiently solved via off-the-shelf algorithms. An example, concerning an application of motion control for robotic arms, shows the effectiveness of the proposed methodology.

Identification and modelling of the friction-induced hysteresis in pneumatic actuators for biomimetic robots

Abstract: Pneumatic Artificial Muscle (PAM) is becoming one of the most used actuator technology for the development of biorobotic applications, such as robotic orthoses and wearable exoskeletons, which require the accurate control of the impedance during human-robot interactions. Although the adaptable compliance of PAMs is desirable, the nonlinear and hysteretic relation between contraction length and pulling force, as well as the air pressure within the chamber of the PAM, make difficult the identification and the control of the dynamics of such actuators. After the description of the experimental setup designed for the dynamic identification of PAMs, this paper presents a novel and accurate model of the hysteresis of the mechanical response of PAMs. Some experimental tests have been performed on a real pneumatic muscle in order to reproduce the different features of the hysteretic behavior which are taken into account in the definition of the model. The proposed model, which has been validated through some experiments, provides some advantages in terms of ease of parameter identification and implementation into a control system, thanks to the use of a limited number of parameters.

Controller Design for the Finite-Time Stabilization of Continuous-Time Linear Systems

Abstract: In this chapter, we consider the finite-time stabilization problem. The starting point is condition (v) in Theorem 2.1, which allows the derivation of a necessary and sufficient condition for the finite-time stabilization via state and output feedback. The technique is then illustrated through the application to the car suspension system example introduced in Sect. 2.5.

Robustness Model Validation of Bistability in Biomolecular Systems

Abstract: Bistability is a key system-level dynamical property to understand the basic mechanisms underpinning some cellular functions, like persistent memory, switch-like biochemical responses and irreversible cell differentiation. These processes are guaranteed by evolved molecular modules, involving genes, proteins and metabolites, which implement transitions between distinct operative conditions in response to exogenous and endogenous signals. In many cases, such a coordinated control action leads to a change in the dynamic behaviour of the cell, which persists even after the activating signal (e.g., the concentration of a certain molecular species) has returned to the initial concentration. A propaedeutical step to the construction of biomodels for this class of systems, is the analysis of the structure of the underlying biochemical reaction network; in particular, a necessary requirement is that the topology of this network is compatible with the assumed bistable Bistablebehaviour. Subsequently, one can face the question of whether the same performance is guaranteed even in the presence of endogenous and exogenous perturbations, i.e., whether the model is robustly bistable Bistablein the face of, e.g., parametric uncertainty (deriving from interindividual variability) or fluctuating environmental conditions (due to the intrinsic stochastic nature of cellular processes). The present chapter focusses on the presentation of methodological approaches for the characterization of bistability in biological systems; such methods are important as tools to assess the plausibility of mathematical models of biosystems that exhibit bimodal experimental behaviour, without recurring to large-scale computational simulations.

FTS of IDLSs

Abstract: In this chapter, we consider the class of CT-LTV systems with finite state jumps, which are linear continuous-time systems whose states undergo finite jump discontinuities at discrete instants of time. Such systems, namely Impulsive Dynamical Linear Systems (IDLSs) (Haddad et al., Impulsive and Hybrid Dynamical Systems, Princeton University Press, Princeton, 2006), can be regarded as a special class of hybrid systems, and they can be either time-dependent (TD-IDLSs) if the state jumps are time-driven or state-dependent (SD-IDLSs) if the state jumps occur when the trajectory reaches an assigned subset of the state space, the so-called resetting set. TD-IDLSs can also be seen as a special case of switching linear systems (Liberzon, Switching in Systems and Control, Springer, Berlin, 2003). Lyapunov stability and stabilization of hybrid systems have been thoroughly discussed in the literature (see, for instance, the monographs Liberzon, Switching in Systems and Control, Springer, Berlin, 2003; Haddad et al., Impulsive and Hybrid Dynamical Systems, Princeton University Press, Princeton, 2006; Pettersson, Analysis and Design of Hybrid Systems. Ph.D. Thesis, 1999, and references therein). In this chapter, we propose some necessary and sufficient conditions for the FTS of TD-IDLSs, while only a sufficient condition will be provided for SD-IDLSs.

FTS Analysis Via PQLFs

Abstract: This chapter deals with the FTS analysis for CT-LTV systems when the initial and trajectory domains are piecewise quadratic. The approaches presented in the previous chapters of the book make use of quadratic Lyapunov functions to perform the FTS analysis and control of a given system. This is consistent with the fact that the initial and trajectory domains have been assumed to be ellipsoidal. The main contribution of this chapter is to consider a more general class of Lyapunov functions, namely the family of Piecewise Quadratic Lyapunov Functions (PQLFs). In particular, a novel sufficient condition for the FTS of CT-LTV systems, based on the PQLFs approach, is provided; then a procedure is proposed to convert such a condition into a computationally tractable problem. The numerical examples included at the end of the chapter are divided into three parts: first, we introduce a comparison with the other results presented in this book when ellipsoidal initial and trajectory domains are considered; then we present an example in which the domains have different structures, that is, a polytopic initial domain and an ellipsoidal trajectory domain; finally, the general case in which both the domains are polytopic is discussed in the third example. In the last two examples, the conditions developed in Chap. 2 can only be applied with added conservativeness due to the necessity of approximating the polytopic domains by ellipsoidal domains.

FTS Analysis of Continuous-Time Linear Systems

Abstract: This chapter deals with the finite-time analysis and design problems for CT-LTV systems. Necessary and sufficient conditions for FTS are provided. One condition is based on the state transition matrix and is of poor usefulness in practice; the other conditions involve either DLMIs or DLEs. It is shown that the DLE-based condition is more efficient from the computational point of view; however, DLMIs are useful in the context of the design problem. Indeed, by the latter approach, we solve both the state and output feedback finite-time stabilization problems. The model of the car suspension system is used as a test case to show the effectiveness of the proposed techniques.

Controller Design for the Finite-Time Stabilization of IDLSs

Abstract: Finite-time stabilization of IDLSs is tackled in this chapter. The D/DLMI feasibility problems introduced in Chap. 7 will be here exploited to derive necessary and sufficient conditions for finite-time stabilization of TD-IDLSs, while only sufficient conditions will be given in the case of SD-IDLSs. In the conclusion section, we will show, by means of some examples, how to extend the presented results to the more general case of time-dependent SLSs.

FTS of Discrete-Time Linear Systems

Abstract: In this chapter, we deal with some finite-time control problems for discrete-time linear time-varying (DT-LTV) systems. First, we provide necessary and sufficient conditions for finite-time stability; such conditions can be regarded as the discrete-time counterparts of the results stated in Theorem 2.1. Indeed, one condition involves the computation of the state transition matrix; the other condition requires the solvability of a difference Lyapunov equality (DLE) or the feasibility of a difference linear matrix inequality (DLMI), respectively. The DLMI condition is the basis for the solution of the state and output feedback problems, which, again, are expressed in terms of optimization problems involving DLMIs.

Robustness Issues for IDLSs

Abstract: This chapter deals with the FTS of uncertain hybrid systems. First, we extend the definition of QFTS given in Chap. 4 to the class of IDLSs subject to norm-bounded uncertainties. Necessary and sufficient conditions to check QFTS are provided for the case of uncertain TD-IDLSs, while only a sufficient condition can be given for SD-IDLSs. The case of switching systems subject to uncertain resetting times is then considered; sufficient conditions to check FTS for the class of SLSs are given.