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The problem of observer design for robust residual generation in nonlinear discrete-time systems is considered. The method is proposed to solve this problem involving nonlinear time-dependent transformation of state-space system model into strict feedback form. To make this transformation practicable, algebra of time-dependent functions is developed.
A class of complex control systems, modelled as a finite family of stochastic differential equations with state-dependent noise is considered. Each individual equation of this family describes the plant state variable in individual regime of the system composed of a set of interconnected subsystems. The transitions between these regimes are discontinuous and are modelled by a homogeneous Markov chain...
An output feedback robust controller based on sliding modes and indirect adaptive control called Indirect Variable Structure Model Reference Adaptive Control (IVS-MRAC) was recently proposed for relative degree one LTI plants, suggesting to be globally asymptotically stable with superior transient behavior and disturbance rejection properties. In this paper, some remarkable simplifications are carried...
In this paper we study certain infinite-dimensional Sylvester equations. The equations are closely related to robust output regulation of infinite-dimensional systems. If the signal generator is finite-dimensional or has discrete spectrum and a complete set of orthonormal eigenvectors, there are some known sufficient conditions for the decomposing of these Sylvester equations. In this paper we generalize...
The fact that the feedback interconnection of strictly positive real (spr) systems leads to an asymptotically stable closed loop can be used for the synthesis of robust observer-based state-space controllers. Since most control plants originally are not spr structural modifications must be done to establish this property even under parameter variations. Going that way one gets a modified spr plant...
We face the problem of stabilizing Linear Parameter Varying systems by means of Gain Scheduling Control. This technique consists on designing a controller which is able to update its parameters on-line according to the variations of the plant parameters. We first consider the state feedback case and we show a design procedure based on the construction of a Lyapunov function for discrete-time LPV systems...
In this paper, H∞ approach is applied in order to design robust controllers for irrigation canals. From an automatic control point of view, an irrigation canal is a strongly coupled multi-variable system. More precisely, it is a cascade of sub-systems (pools) where the control input of each sub-system perturbs the previous sub-system. Control laws are usually obtained by designing monovariable controllers...
For both continuous and discrete-time cases, this paper presents a simple solution to the robust H∞ unbiased functional reduced order filtering problem via LMI methods in the presence of norm-bounded time-varying uncertainties. Necessary and sufficient conditions for the existence and the stability of the unbiased filter are given in the nominal case; the filter differs from that of 11] (only nominal...
In this paper, we propose a set-valued filtering algorithm for non-linear discrete-time systems. At each step, the algorithm computes an ellipsoid of minimal size that guarantees to contain the true state of the system, despite the noise affecting the system and taking into explicit consideration the linearization error. The filter is based on a two-step prediction-correction structure, each step...
In this paper we consider the problem of minimizing the H∞-norm of the sum of two systems which are interconnected with two different controller components. We sketch two specific applications of this decentralized control problem. As the main contribution, we reveal that this structured controller design problem admits a full LMI solution if only one of the systems in the interconnection obeys a...
This report presents a study on the problem of residual evaluation and threshold computation for detection of faults in continuous time nonlinear systems. A generalized framework for designing norm-based residual evaluation scheme is proposed. The problem of threshold computation is formulated as an optimization problem and its solution is developed using the well known LMI technique. Three commonly...
In this note we extend the design tool presented in [6] for robust stabilization of nonminimum-phase nonlinear systems to the case of output regulation problems. As in [6] we take advantage from a design tool known in the linear literature as “vibrational feedback” to handle the presence of unstable zero dynamics in output regulation problems in presence of uncertainties. This work frames in a research...
Previously, a nonlinear passivity control has been proposed for a discrete-time (neutrally) stable bilinear system. However, the decay rate of the closed-loop system is not exponential. In this paper, a new nonlinear control is suggested to achieve exponential decay rate. It is also shown that the new control is robust against small parametric uncertainties.
In this paper, robust fault detection using a parity equation passive robust approach based on generating an adaptive threshold considering that the system to be monitored can be described by an interval linear parameter varying (LPV) model with variable transport delay is proposed. This approach allows to consider parameters and associated uncertainty intervals dependence on the operating point....
Several approaches have been taken to estimate the fundamental frequency of periodic or pseudoperiodic acoustic signals. However, since the algorithms operate in different transform domains, it has proven difficult to combine the desirable features of different algorithms, and to utilize simulation results across domains. In this paper, we set out to define a common ground on which to investigate...
A nonlinear robust state feedback controller is presented for the minimization of water level deviation in presence of disturbances in a one-reach open channel controlled by an underflow gate at the upstream end. To apply nonlinear robust control to this distributed parameter system, the original nonlinear partial differential equations (the Saint-Venant equations) were adopted without using neither...
A general question one has to face in the study of an optimal control problem is the representation of the closure of the set of trajectories. Loosely speaking, two main problems lie at the basis of the non triviality of this question: the lack of sufficient convexity assumptions (which is at the origin of the introduction of the so-called chattering controls) and the occurrence of unbounded controls...
The paper presents some results on parametric identification of linear systems applied to robust Fault Diagnosis schemes. In our approach, an equation error model is derived from input- output data. In particular, the error term takes into account disturbances (non measurable inputs), nonlinear and time-variant terms, measurement errors, etc. In this manner, state-space realization of the equation...
Well-posedness of feedback connected systems is considered in topological separation framework. The case when a known linear descriptor transformation is connected to an uncertain operator is considered. Well-posedness is demonstrated to hold provided an Integral Quadratic Separator satisfying both some Linear Matrix Inequalities and an Integral Quadratic Constraint. The main result is applied to...
This article presents an application of a control strategy developed by the authors to a nonlinear model. The control strategy is based on a sliding mode controller that uses a generalized predictive controller for the reaching mode part. The proposed Predictive Sliding Mode Controller is developed for a First-Order-Plus-Deadtime model that represents a good approximation to many processes. The Predictive...
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