summary:It is known that for affine nonlinear systems the drift-observability property (i. e. obs... more summary:It is known that for affine nonlinear systems the drift-observability property (i. e. observability for zero input) is not sufficient to guarantee the existence of an asymptotic observer for any input. Many authors studied structural conditions that ensure uniform observability of nonlinear systems (i. e. observability for any input). Conditions are available that define classes of systems that are uniformly observable. This work considers the problem of state observation with exponential error rate for smooth nonlinear systems that meet or not conditions of uniform observability. In previous works the authors showed that drift-observability together with a smallness condition on the input is sufficient to ensure existence of an exponential observer. Here it is shown that drift- observability implies a kind of local uniform observability, that is observability for sufficiently small and smooth input. For locally uniformly observable systems two observers are presented: an ex...
State observers for nonlinear systems with output delayed information
1999 European Control Conference (ECC), 1999
The problem of state observation for nonlinear systems in which the output measurement is accessi... more The problem of state observation for nonlinear systems in which the output measurement is accessible after some time delay is studied in this paper, and an observer is proposed for the unforced case. On this matter no results, to our knowledge, are available in literature. The proposed observer is a nonlinear delay system and is an identity observer, in that it reproduces exactly the system equation when initialized by the true initial state. Its implementation is easy and computer simulations show its effectiveness. When the delay is equal to zero, this algorithm is equal to the one for nonlinear systems in [9]. Sufficient conditions are obtained that ensure convergence to zero of the observation error for any output delay.
This paper considers the¯ltering and identi¯cation problems for a class of discrete-time uncertai... more This paper considers the¯ltering and identi¯cation problems for a class of discrete-time uncertain stochastic systems that admit a¯nite number of linear working modes. It is shown here that this class of uncertain systems can be modeled by using a suitably de¯ned extended system, whose state evolves according to a bilinear model. A polynomial¯ltering algorithm is derived for such extended system, which readily provides the polynomial estimates of both the original state and the working mode. Simulations show the e®ectiveness of the proposed approach and the improvements with respect to standard linear¯ltering algorithms.
This work presents a family of polynomial¯lters for discrete-time nonlinear stochastic systems. T... more This work presents a family of polynomial¯lters for discrete-time nonlinear stochastic systems. These¯lters can be considered the polynomial version of the well known Extended Kalman Filter. The standard EKF consists in the optimal linear¯lter applied to the linear approximation of systems. The¯lters presented in this paper are polynomial¯lters applied to polynomial approximations of nonlinear systems, and therefore each of them is characterized by a pair of integers: the degree of the system approximation and the degree of the¯lter. The¯rst¯lter of the family, the one of order (1,1), coincides with the EKF in the standard form. The implementation of the proposed¯lters does not require the complete knowledge of the noise distributions, but only the moments up to suitable orders. Numerical simulations show the performances of the¯lters for some values of the degrees. Copyright c°2005 IFAC
The aim of this paper is to investigate the problem of the joint estimation of both the state and... more The aim of this paper is to investigate the problem of the joint estimation of both the state and parameters for a class of discrete-time linear systems driven by additive noise, not necessarily Gaussian. A recursive quadratic filter with respect to the observations is here proposed and implemented, by opportunely extending the state space also with the inclusion of the
Observer-Based Stabilizing Control for a Class of Nonlinear Retarded Systems
Lecture Notes in Control and Information Sciences, 2012
ABSTRACT Stabilizing cascade observer-controller schemes for a class of nonlinear retarded system... more ABSTRACT Stabilizing cascade observer-controller schemes for a class of nonlinear retarded systems are presented in this chapter. Conditions for the local and global asymptotic stability of the closed loop system are provided. Such conditions allow the separate design of the observer and of the controller subsystems (separation theorems).
This paper introduces a new filter for linear continuous-time stochastic systems with delayed mea... more This paper introduces a new filter for linear continuous-time stochastic systems with delayed measurements. The approach is inspired by an observer designed for deterministic systems. The obtained solution is suboptimal and does not use distributed integration terms with advantages in terms of computational load. The relationship between the delay bound and the variance of the estimation error is formally characterized and confirmed by a numerical example.
Proceedings of the 45th IEEE Conference on Decision and Control, 2006
This note presents an approach for the design of asymptotic state observers for systems character... more This note presents an approach for the design of asymptotic state observers for systems characterized by output functions that are ratios of polynomials in the state. The case of linear and bilinear input-state dynamics is considered, and conditions for exponential error decay are provided. The first step towards the construction of the observer is to show that the dynamics of a system in the considered class can be embedded into the dynamics of a system of higher dimension, with time-varying linear state dynamics and linear output map. The construction of the observer here proposed exploits the structure of the extended system. The solution of a Riccati differential equation provides the observer gain.
In this paper global and local separation theorems for a class of retarded nonlinear systems are ... more In this paper global and local separation theorems for a class of retarded nonlinear systems are investigated. Copyright @ IFAC
Filtering Continuous-Time Linear Systems With Time-Varying Measurement Delay
IEEE Transactions on Automatic Control, 2015
We consider the filtering problem of LTI continuous-time systems with known and bounded measureme... more We consider the filtering problem of LTI continuous-time systems with known and bounded measurement delays. The aim of the technical note is the design of a finite-dimensional sub-optimal filter whose performance in terms of the estimation error is comparable to optimal infinite-dimensional approaches. We show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error. In the time-varying case no restrictive hypotheses on the delay function are needed. The proposed filter can therefore be applied to delay functions for which traditional infinite-dimensional approaches cannot be straightforwardly applied.
In this paper it is studied the classical problem of target tracking by a new approach consisting... more In this paper it is studied the classical problem of target tracking by a new approach consisting in the treatment of the classical nonlinear measurement process in a form amenable for polynomial filtering without the need of the measure map linearization, as required by other standard sub-optimal algorithms. The main idea is to transfer the nonlinearity of the measure map into a modification of the noise sequence distribution in a nongaussian white sequence. This is indeed the property required for Kalman filtering which, although non more optimal, remains to be the optimal linear filtering algorithm. Conditions for polynomial filtering are also satisfied, allowing to face the nongaussian nature of the modified noise sequence. Simulations show high performances of the proposed algorithm.
summary:It is known that for affine nonlinear systems the drift-observability property (i. e. obs... more summary:It is known that for affine nonlinear systems the drift-observability property (i. e. observability for zero input) is not sufficient to guarantee the existence of an asymptotic observer for any input. Many authors studied structural conditions that ensure uniform observability of nonlinear systems (i. e. observability for any input). Conditions are available that define classes of systems that are uniformly observable. This work considers the problem of state observation with exponential error rate for smooth nonlinear systems that meet or not conditions of uniform observability. In previous works the authors showed that drift-observability together with a smallness condition on the input is sufficient to ensure existence of an exponential observer. Here it is shown that drift- observability implies a kind of local uniform observability, that is observability for sufficiently small and smooth input. For locally uniformly observable systems two observers are presented: an ex...
State observers for nonlinear systems with output delayed information
1999 European Control Conference (ECC), 1999
The problem of state observation for nonlinear systems in which the output measurement is accessi... more The problem of state observation for nonlinear systems in which the output measurement is accessible after some time delay is studied in this paper, and an observer is proposed for the unforced case. On this matter no results, to our knowledge, are available in literature. The proposed observer is a nonlinear delay system and is an identity observer, in that it reproduces exactly the system equation when initialized by the true initial state. Its implementation is easy and computer simulations show its effectiveness. When the delay is equal to zero, this algorithm is equal to the one for nonlinear systems in [9]. Sufficient conditions are obtained that ensure convergence to zero of the observation error for any output delay.
This paper considers the¯ltering and identi¯cation problems for a class of discrete-time uncertai... more This paper considers the¯ltering and identi¯cation problems for a class of discrete-time uncertain stochastic systems that admit a¯nite number of linear working modes. It is shown here that this class of uncertain systems can be modeled by using a suitably de¯ned extended system, whose state evolves according to a bilinear model. A polynomial¯ltering algorithm is derived for such extended system, which readily provides the polynomial estimates of both the original state and the working mode. Simulations show the e®ectiveness of the proposed approach and the improvements with respect to standard linear¯ltering algorithms.
This work presents a family of polynomial¯lters for discrete-time nonlinear stochastic systems. T... more This work presents a family of polynomial¯lters for discrete-time nonlinear stochastic systems. These¯lters can be considered the polynomial version of the well known Extended Kalman Filter. The standard EKF consists in the optimal linear¯lter applied to the linear approximation of systems. The¯lters presented in this paper are polynomial¯lters applied to polynomial approximations of nonlinear systems, and therefore each of them is characterized by a pair of integers: the degree of the system approximation and the degree of the¯lter. The¯rst¯lter of the family, the one of order (1,1), coincides with the EKF in the standard form. The implementation of the proposed¯lters does not require the complete knowledge of the noise distributions, but only the moments up to suitable orders. Numerical simulations show the performances of the¯lters for some values of the degrees. Copyright c°2005 IFAC
The aim of this paper is to investigate the problem of the joint estimation of both the state and... more The aim of this paper is to investigate the problem of the joint estimation of both the state and parameters for a class of discrete-time linear systems driven by additive noise, not necessarily Gaussian. A recursive quadratic filter with respect to the observations is here proposed and implemented, by opportunely extending the state space also with the inclusion of the
Observer-Based Stabilizing Control for a Class of Nonlinear Retarded Systems
Lecture Notes in Control and Information Sciences, 2012
ABSTRACT Stabilizing cascade observer-controller schemes for a class of nonlinear retarded system... more ABSTRACT Stabilizing cascade observer-controller schemes for a class of nonlinear retarded systems are presented in this chapter. Conditions for the local and global asymptotic stability of the closed loop system are provided. Such conditions allow the separate design of the observer and of the controller subsystems (separation theorems).
This paper introduces a new filter for linear continuous-time stochastic systems with delayed mea... more This paper introduces a new filter for linear continuous-time stochastic systems with delayed measurements. The approach is inspired by an observer designed for deterministic systems. The obtained solution is suboptimal and does not use distributed integration terms with advantages in terms of computational load. The relationship between the delay bound and the variance of the estimation error is formally characterized and confirmed by a numerical example.
Proceedings of the 45th IEEE Conference on Decision and Control, 2006
This note presents an approach for the design of asymptotic state observers for systems character... more This note presents an approach for the design of asymptotic state observers for systems characterized by output functions that are ratios of polynomials in the state. The case of linear and bilinear input-state dynamics is considered, and conditions for exponential error decay are provided. The first step towards the construction of the observer is to show that the dynamics of a system in the considered class can be embedded into the dynamics of a system of higher dimension, with time-varying linear state dynamics and linear output map. The construction of the observer here proposed exploits the structure of the extended system. The solution of a Riccati differential equation provides the observer gain.
In this paper global and local separation theorems for a class of retarded nonlinear systems are ... more In this paper global and local separation theorems for a class of retarded nonlinear systems are investigated. Copyright @ IFAC
Filtering Continuous-Time Linear Systems With Time-Varying Measurement Delay
IEEE Transactions on Automatic Control, 2015
We consider the filtering problem of LTI continuous-time systems with known and bounded measureme... more We consider the filtering problem of LTI continuous-time systems with known and bounded measurement delays. The aim of the technical note is the design of a finite-dimensional sub-optimal filter whose performance in terms of the estimation error is comparable to optimal infinite-dimensional approaches. We show that the proposed approach allows for a precise characterization of the relationship between measurement delay and the covariance of the estimation error. In the time-varying case no restrictive hypotheses on the delay function are needed. The proposed filter can therefore be applied to delay functions for which traditional infinite-dimensional approaches cannot be straightforwardly applied.
In this paper it is studied the classical problem of target tracking by a new approach consisting... more In this paper it is studied the classical problem of target tracking by a new approach consisting in the treatment of the classical nonlinear measurement process in a form amenable for polynomial filtering without the need of the measure map linearization, as required by other standard sub-optimal algorithms. The main idea is to transfer the nonlinearity of the measure map into a modification of the noise sequence distribution in a nongaussian white sequence. This is indeed the property required for Kalman filtering which, although non more optimal, remains to be the optimal linear filtering algorithm. Conditions for polynomial filtering are also satisfied, allowing to face the nongaussian nature of the modified noise sequence. Simulations show high performances of the proposed algorithm.
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