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In this paper a novel control method for geometric invariance control is proposed. Nonlinear SISO systems with unstable internal dynamics can be stabilized. In variance conditions of a given state space region are discussed. Sufficient conditions for an output stabilizing Lyapunov controller to assure invariance ofthat region are derived. Simulations of an underactuated, non-minimum phase example...
In this note we propose a new persistency of excitation condition for stability of nonlinear time-varying (NLTV) systems, which applies to adaptive systems with state-dependent regressor signals. We give sufficient conditions for uniform global asymptotic stability (UGAS). This result gives a transparent interpretation to the time-varying stabilization mechanism for nonholonomic systems. For 3-degrees-of-freedom...
A general invariance principle is proposed from the output-to-state view-point for general nonlinear time-varying systems. A simple and intuitive criterion is proposed using an integral inequality involving the output function and a modified detectability condition. When applied to systems having a Lyapunov function, the well-known LaSalle's invariance principle can be deduces based on our approach...
The notion of generally quasipassive system is introduced. It is shown that for affine nonlinear control systems the general quasipassivity property plus output-to-state stability under zero input plus nonnegativity of certain pseudoscalar product of storage function's and OSS-Lyapunov function's differentials implies the existence of output feedback making the closed loop system UB. The result gives...
The notions of strong and weak synchronization of chaotic systems are reviewed in the context of three coupled identical one-dimensional maps. Two possibilities exist. Either all three systems synchronize (total synchronization), or only two out of three systems synchronize (partial synchronization, or clustering). In either case, strong and weak synchronization is possible.
In this paper we design a position controller for an autonomous mobile robot, a nonlinear nonholonomic control system. The designed time invariant non smooth stabilizing control law assures limitation of the velocity inputs, human like driving behaviour and smooth trajectories. The global asymptotic stability of the closed loop system is proved using the Lyapunov stability theory and the In-variance...
Given an interval matrix system with discrete- or continuous-time dynamics, the flow-invariance of an arbitrarily time-dependent rectangular set with respect to this system is introduced as a concept of geometric nature. The case of rectangular sets with exponential time-dependence is separately explored. If there exist flow-invariant rectangular sets approaching the state space origin for an infinite...
In this note it is shown how the n-dimensional rigid body equation naturally leads to Hamilton's canonical equation and how this may be used for controller and observer designs by using the geometry of mechanical systems on manifolds avoiding the parameterization of Lie group SO(n). Based on this approach, it is possible to focus on the intrinsic property of the system and to show closed-loop stability,...
In this paper we study the tracking control of Lagrangian systems subject to frictionless unilateral constraints. The stability analysis incorporates the hybrid and nonsmooth dynamical feature of the overall system. The difference between tracking control for unconstrained systems and unilaterally constrained ones, is explained in terms of closed-loop desired trajectories and control signals. This...
New results of qualitative analysis are presented for a class of neural networks (Hopfield-type), representing a refinement in the interpretation of their behaviour. The main instrument of this analysis consists in the individual monitoring of the state-trajectories by considering time-dependent rectangular sets that are forward invariant with respect to the dynamics of the investigated systems. Particular...
Recent methods for gain scheduling controller design based on linear parameter-varying (LPV) systems offer a systematic way to obtain a nonlinear controller that covers different operating conditions. However, despite that the LPV synthesis part of the process of obtaining a gain scheduled controller is theoretically straight forward, the nonlinear closed loop system may be unstable for some operating...
The asymptotic behaviour of the optimal cost for problems with increasing time horizon is studied. The dynamics and costs are general nonlinear, possibly with state and control constraints. Apart from basic consistency assumptions, a uniform detectability hypothesis provides the setup for the analysis, which is based on direct evaluations of bounds for costs and trajectories. This investigation is...
An switching adaptive control scheme is presented, which provides global asymptotic stability property with respect to state space vector of the plant. In the presence of disturbance these schemes ensure boundedness of all trajectories of the system.
We present new characterizations of integral Input-Output-to-State Stability. This is a notion of dectectability formulated in the Input-to-State Stability framework. Equivalent properties are discussed in terms Lyapunov dissipation inequalities and asymptotic estimates of the state variables on the basis of external information provided by input and output signals.
This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS and to study its convergence rate. We show that this property of being GUAS is equivalent to the uniform observability on [0, +∞) of a bilinear system defined on a subspace whose...
In this paper, two stabilizing nonlinear model predictive control (NMPC) designs, namely, final-state equality constraint stabilizing design and final-state inequality constraint stabilizing design have been applied to achieve two wheeled mobile robot's control objectives, i.e. point stabilization and trajectory tracking. In both controllers, final-state constraints are imposed, on the online optimization...
We study the stability of the origin for the dynamical system x(t) = u(t)Ax(t) + (1 − u(t))Bx(t), where A and B are two 2×2 real matrices with eigenvalues having strictly negative real part, x ∊ R2 and u(.) : [0, ∞[→ [0,1] is a completely random measurable function. More precisely, we find a (coordinates invariant) necessary and sufficient condition on A and B for the origin to be asymptotically stable...
The problem of input-to-output stability for switched nonlinear systems is considered. Two approaches for switching between non-exponentially stable systems are proposed guaranteeing input-to-output stability for the switched system.
In this contribution we analyze in detail the stability of the linear dynamic output feedback which has been introduced in [1], [2] for the stabilization of trajectories for differentially flat systems and which has been extended to nonflat systems whose linearization about the reference trajectory is controllable [3], [4]. The linearized tracking error dynamics of the closed loop system are shown...
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