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We consider control systems of the type x?? = Ax+??(t)ub, where u ?? R, (A; b) is a controllable pair and ?? is an unknown time-varying signal with values in [0; 1] satisfying a permanent excitation condition of the kind ??t+Tt ?? ?? ??for 0 < ?? ?? T independent on t. We prove that such a system is stabilizable with a linear feedback depending only on the pair (T; ??) if the real part of the...
The presented work addresses the observation problem for a large class of nonlinear systems, including systems which are nonlinear in the unmeasured states. Assuming partial state measurements, the unmeasured states are reconstructed so that a prediction of the measured states converges to a neighborhood of the actual measurements. This prediction-based observer algorithm relies on carefully selected...
In this paper, we study the discrete-time nonlinear consensus protocols over both directed and undirected networks with fixed topology. First, the notions of (global/exponential) semistability are introduced for systems with a continuum of equilibria. In terms of (global/exponential) consensus defined based on the notion of semistability, we have derived convergence conditions for the general discrete-time...
This paper presents the application of iterative learning control (ILC) to compensate hysteresis in a piezoelectric actuator. The proposed controller is a hybrid of proportional-integral-differential (PID) control, whose main function is for trajectory tracking, and a chatter-based ILC, whose main function is for hysteresis compensation. Stability analysis of the proposed ILC is presented, with the...
A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative. In this...
Motion control systems have found their application in various industry products. Common issues encountered when designing this type of systems are nonlinearities and uncertainties (e.g., unknown parameters, unmodeled dynamics, and disturbances). In this paper, we study controller design for a class of motion systems with rotary components. The systems are assumed to have unknown parameters which...
The traditional model reference adaptive system (MRAS) is of parallel configuration. By representing the reference model as an equivalent closed-loop subsystem, these two subsystems can share a controller virtually. An embedded structure of MRAS is thereby presented. In this paper, two approaches are developed for designing the adaptive laws. The adaptive law based on Lyapunov stability theory is...
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