Fault-tolerant control under controller-driven sampling using virtual actuator strategy

We present a new output feedback fault tolerant control strategy for continuous-time linear systems. The strategy combines a digital nominal controller under controller-driven (varying) sampling with virtual-actuator (VA)-based controller reconfiguration to compensate for actuator faults. In the proposed scheme, the controller controls both the plant and the sampling period, and performs controller reconfiguration by engaging in the loop the VA adapted to the diagnosed fault. The VA also operates under controller-driven sampling. Two independent objectives are considered: (a) closed-loop stability with setpoint tracking and (b) controller reconfiguration under faults. Our main contribution is to extend an existing VA-based controller reconfiguration strategy to systems under controller-driven sampling in such a way that if objective (a) is possible under controller-driven sampling (without VA) and objective (b) is possible under uniform sampling (without controller-driven sampling), then closed-loop stability and setpoint tracking will be preserved under both healthy and faulty operation for all possible sampling rate evolutions that may be selected by the controller

Optimal Robust Exact Differentiation via Linear Adaptive Techniques

The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal differentiators, in terms of the smallest achievable worst-case differentiation error, are shown. A robust exact differentiator is then constructed via the adaptation of a single parameter of a linear differentiator. It is demonstrated that the resulting differentiator exhibits a combination of properties that outperforms existing continuous-time differentiators: it is robust with respect to noise, it instantaneously converges to the exact derivative in the absence of noise, and it attains the smallest possible -- hence optimal -- upper bound on its differentiation error under noisy measurements. For sample-based differentiators, the concept of quasi-exactness is introduced to classify differentiators that achieve the lowest possible worst-case error based on sampled measurements in the absence of noise. A straightforward sample-based implementation of the proposed linear adaptive continuous-time differentiator is shown to achieve quasi-exactness after a single sampling step as well as a theoretically optimal differentiation error bound that, in addition, converges to the continuous-time optimal one as the sampling period becomes arbitrarily small. A numerical simulation illustrates the presented formal results

Large-signal stability conditions for semi-quasi-Z-source inverters: switched and averaged models

The recently introduced semi-quasi-Z-source in- verter can be interpreted as a DC-DC converter whose input- output voltage gain may take any value between minus infinity and 1 depending on the applied duty cycle. In order to generate a sinusoidal voltage waveform at the output of this converter, a time-varying duty cycle needs to be applied. Application of a time-varying duty cycle that produces large-signal behavior requires careful consideration of stability issues. This paper provides stability results for both the large-signal averaged and the switched models of the semi-quasi-Z-source inverter operating in continuous conduction mode. We show that if the load is linear and purely resistive then the boundedness and ultimate boundedness of the state trajectories is guaranteed provided some reasonable operation conditions are ensured. These conditions amount to keeping the duty cycle away from the extreme values 0 or 1 (averaged and switched models), and limiting the maximum PWM switching period (switched model). The results obtained can be used to give theoretical justification to the inverter operation strategy recently proposed by Cao et al. in [1].Comment: Submitted to the IEEE Conf. on Decision and Control, Florence, Italy, 201

Bounds and Invariant Sets for a Class of Switching Systems with Delayed-state-dependent Perturbations

We present a novel method to compute componentwise transient bounds, ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The main advantage of the method is its componentwise nature, i.e. the fact that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise. This componentwise method does not employ a norm for bounding either the perturbation or state vectors, avoids the need for scaling the different state vector components in order to obtain useful results, and may also reduce conservativeness in some cases. We give conditions for the derived bounds to be of local or semi-global nature. In addition, we deal with the case of perturbation bounds whose dependence on a delayed state is of affine form as a particular case of nonlinear dependence for which the bounds derived are shown to be globally valid. A sufficient condition for practical stability is also provided. The present paper builds upon and extends to switching systems with delayed-state-dependent perturbations previous results by the authors. In this sense, the contribution is three-fold: the derivation of the aforementioned extension; the elucidation of the precise relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic Lyapunov function (a question that was left open in our previous work); and the derivation of a technique to compute a common quadratic Lyapunov function for switching linear systems with perturbations bounded componentwise by affine functions of the absolute value of the state vector components.Comment: Submitted to Automatic

Time-delay systems that defy intuition: nonrobust forward completeness and related (non)properties

An example of a time-invariant time-delay system that is uniformly globally attractive and Lyapunov stable, hence forward complete, but whose reachability sets from bounded initial conditions are not bounded over compact time intervals is provided. This gives a negative answer to two current conjectures by showing that (i) forward completeness is not equivalent to robust forward completeness and (ii) global asymptotic stability is not equivalent to uniform global asymptotic stability. In addition, a novel characterization of robust forward completeness for usually encountered classes of time-delay systems is provided. This characterization relates robust forward completeness of the time-delay system with the forward completeness of an associated nondelayed finite-dimensional system.Comment: Submitted to Automatica. Print ISSN: 0005-1098, Online ISSN: 1873-283

Robust exact differentiators with predefined convergence time

The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded convergence time. A tuning procedure is derived that allows to assign an arbitrary, predefined upper bound for this convergence time. It is furthermore shown that this bound can be made arbitrarily tight by appropriate tuning. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which the considered class of differentiators includes as a special case

Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models

Several control design strategies for sampled-data systems are based on a discrete-time model. In general, the exact discrete-time model of a nonlinear system is difficult or impossible to obtain, and hence approximate discrete-time models may be employed. Most existing results provide conditions under which the stability of the approximate discrete-time model in closed-loop carries over to the stability of the (unknown) exact discrete-time model but only in a practical sense, meaning that trajectories of the closed-loop system are ensured to converge to a bounded region whose size can be made as small as desired by limiting the maximum sampling period. In addition, some sufficient conditions exist that ensure global exponential stability of an exact model based on an approximate model. However, these conditions may be rather stringent due to the global nature of the result. In this context, our main contribution consists in providing rather mild conditions to ensure semiglobal exponential input-to-state stability of the exact model via an approximate model. The enabling condition, which we name the Robust Equilibrium-Preserving Consistency (REPC) property, is obtained by transforming a previously existing consistency condition into a semiglobal and perturbation-admitting condition. As a second contribution, we show that every explicit and consistent Runge-Kutta model satisfies the REPC condition and hence control design based on such a Runge-Kutta model can be used to ensure semiglobal exponential input-to-state stability of the exact discrete-time model in closed loop.Comment: 10 page

Simultaneous Triangularization of Switching Linear Systems: Arbitrary Eigenvalue Assignment and Genericity

A sufficient condition for the stability of arbitrary switching linear systems (SLSs) without control inputs is that the individual subsystems are stable and their evolution matrices are simultaneously triangularizable (ST). This sufficient condition for stability is known to be extremely restrictive and not robust, and therefore of very limited applicability. The situation can be radically different when control inputs are present. Indeed, previous results have established that, depending on the number of states, inputs and subsystems, the existence of feedback matrices for each subsystem so that the corresponding closed-loop matrices are stable and ST can become a generic property, i.e., a property valid for almost every set of system parameters. This note provides novel contributions along two lines. First, we give sufficient conditions for the genericity of the property of existence of feedback matrices so that the subsystem closed-loop matrices are ST (not necessarily stable). Second, we give conditions for the genericity of the property of existence of feedback matrices that, in addition to achieving ST, enable arbitrary eigenvalue selection for each subsystem's closed-loop matrix. The latter conditions are less stringent than existing ones, and the approach employed in their derivation can be interpreted as an extension to SLSs of specific aspects of the notion of eigenvalue controllability for (non-switching) linear systems.Fil: Haimovich, Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas. Universidad Nacional de Rosario. Centro Internacional Franco Argentino de Ciencias de la Información y de Sistemas; Argentin