Active state estimation of nonlinear systems

In this paper, state observers for control systems with nonlinear outputs are studied. For such systems, the observability does not only depend on the initial conditions, but also on the exciting control used. Thus, for such systems, design of active control is an integral part of the design for state observers. Here some sufficient conditions are given for the convergence of an observer. It is also discussed, via a camera example, how to actively excite a system in order to improve the observability.     

Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes

A moving-horizon state estimation problem is addressed for a class of nonlinear discrete-time systems with bounded noises acting on the system and measurement equations. As the statistics of such disturbances and of the initial state are assumed to be unknown, we use a generalized least-squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding-window strategy. For the resulting estimator, the existence of bounding sequences on the estimation error is proved. In the absence of noises, exponential convergence to zero is obtained. Moreover, suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value. The approximate solution can be determined either on-line by directly minimizing the cost function or off-line by using a nonlinear parameterized function. Simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended Kalman filter.     

Suboptimal control for nonlinear systems: a successive approximation approach

This paper presents a successive approximation approach (SAA) designing optimal controllers for a class of nonlinear systems with a quadratic performance index. By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. By using the finite-step iteration of the nonlinear compensation sequence, we can obtain a suboptimal control law. Simulation examples are employed to test the validity of the SAA.     

Adaptive neural control with fast approximation for uncertain nonlinear systems: A novel composite learning approach

In existing adaptive neural control approaches, only when the regressor satisfies the persistent excitation (PE) or interval excitation (IE) conditions, the constant optimal weights of neural network (NN) can be identified, which can be used to establish uncertainties in nonlinear systems. This paper proposes a novel composite learning approach based on adaptive neural control. The focus of this approach is to make the NN approximate uncertainties in nonlinear systems quickly and accurately without identifying the constant optimal weights of the NN. Hence, the regressor does not need to satisfy the PE or IE conditions. In this paper, regressor filtering scheme is adopted to generate prediction error, and then the prediction error and tracking error simultaneously drive the update of NN weights. Under the framework of Lyapulov theory, the proposed composite learning approach can ensure that approximation error of the uncertainty and tracking error of the system states converge to an arbitrarily small neighborhood of zero exponentially. The simulation results verify the effectiveness and advantages of the proposed approach in terms of fast approximation.     

Estimation of nonlinear systems via a Chebyshev approximation approach

This paper proposes to decompose the nonlinear dynamic of a chaotic system with Chebyshev polynomials to improve performances of its estimator. More widely than synchronization of chaotic systems, this algorithm is compared to other nonlinear stochastic estimator such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Chebyshev polynomials orthogonality properties is used to fit a polynomial to a nonlinear function. This polynomial is then used in an Exact Polynomial Kalman Filter (ExPKF) to run real time state estimation. The ExPKF offers mean square error optimality because it can estimate exact statistics of transformed variables through the polynomial function. Analytical expressions of those statistics are derived so as to lower ExPKF algorithm computation complexity and allow real time applications. Simulations under the Additive White Gaussian Noise (AWGN) hypothesis, show relevant performances of this algorithm compared to classical nonlinear estimators.     

A bounded-error approach to simultaneous state and actuator fault estimation for a class of nonlinear systems

This paper proposes an approach for the joint state and fault estimation for a class of uncertain nonlinear systems with simultaneous unknown input and actuator faults. This is achieved by designing an unknown input observer combined with a set-membership estimation in the presence of disturbances and measurement noise. The observer is designed using quadratic boundedness approach that is used to overbound the estimation error. Sufficient conditions for the existence and stability of the proposed state and actuator fault estimator are expressed in the form of linear matrix inequalities (LMIs). Simulation results for a quadruple-tank system show the effectiveness of the proposed approach.     

Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems

This paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter structure, and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous-time and discrete-time nonlinear stochastic systems. Sufficient conditions are given in terms of the solvability of LMIs. Moreover, we also introduce a suboptimal design approach to optimizing the upper bound of the mean-square error of parameter estimation. This suboptimal design procedure is also realized by LMI computations. By a martingale method, we also show that the related Lyapunov function has a non-negative Lyapunov exponent.     

Exact and approximate state estimation for nonlinear dynamic systems

This paper presents a modified approach to solve state estimation problems of nonlinear dynamic systems involving noise free, uncorrelated and correlated state and measurement noise processes. The basic approach makes use of the matrix minimum principle together with the Kolmogorov and Kushner's equations to minimize the error-variance, taken to be the estimation criterion. The filtering equations obtained for nonlinear systems with white noise process are exact, but for non-white noise processes the results obtained are approximate.

For systems with polynomial or product types non-linearities, the proposed algorithms can be evaluated without the need of approximation under the assumption that the estimator errors are Gaussian. Such an assumption is significantly different from the most commonly used assumption that the state is Gaussian. Simulation results obtained from the proposed filtering algorithms are compared to various other approximate nonlinear filters. The results indicate the superiority of the proposed filter over those of other filters investigated.     

Optimal state estimation for stochastic systems: an informationtheoretic approach

In this paper, we examine the problem of optimal state estimation or filtering in stochastic systems using an approach based on information theoretic measures. In this setting, the traditional minimum mean-square measure is compared with information theoretic measures, Kalman filtering theory is reexamined, and some new interpretations are offered. We show that for a linear Gaussian system, the Kalman filter is the optimal filter not only for the mean-square error measure, but for several information theoretic measures which are introduced in this work. For nonlinear systems, these same measures generally are in conflict with each other, and the feedback control policy has a dual role with regard to regulation and estimation. For linear stochastic systems with general noise processes, a lower bound on the achievable mutual information between the estimation error and the observation are derived. The properties of an optimal (probing) control law and the associated optimal filter, which achieve this lower bound, and their relationships are investigated. It is shown that for a linear stochastic system with an affine linear filter for the homogeneous system, under some reachability and observability conditions, zero mutual information between estimation error and observations can be achieved only when the system is Gaussian     

非线性时滞系统次优控制的逐次逼近法

对状态变量含有时滞的非线性系统的次优控制问题进行了研究，提出了一种次优控制的逐次逼近设计方法．针对由最优控制理论导出的既含有时滞项又含有超前项的非线性两点边值问题，构造了其解序列一致收敛于原问题最优解的非齐次线性两点边值问题序列．从而将两点边值问题解序列的有限次迭代结果作为系统的次优控制律．仿真结果表明了所提出方法的有效性．     

Successive approximation approach of optimal control for nonlinear discrete-time systems

A successive approximation approach designing optimal controller is developed for affine nonlinear discrete-time systems with a quadratic performance index. By using this approach the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems. The optimal control law consists of an accurate linear term and a nonlinear compensating term which is the limit of a sequence of adjoint vectors. By taking a finite-time iteration instead of the limit of the sequence of adjoint vectors, we obtain a suboptimal control law. Simulation examples are employed to verify the validity of the proposed algorithm.     

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.     

Event-triggered state estimation for nonlinear systems aid by machine learning

The event-triggered state estimation problem with the aid of machine learning for nonlinear systems is considered in this paper. First, we develop a recurrent neural network (RNN) model to predict the nonlinear systems. Second, we design a discrete-time dynamic event-triggered mechanism (ETM) and a state observer based on this ETM for the prediction model. This discrete-time dynamic event-triggered state observer significantly reduces the utilization of communication resources. Third, we establish a sufficient condition to ensure that the state observer can robustly estimate the state vector of the RNN model. Finally, we provide an illustrative example to verify the merit of the obtained results.     

Constrained state estimation for stochastic jump systems: moving horizon approach

We discuss the state estimation advantages for a class of linear discrete-time stochastic jump systems, in which a Markov process governs the operation mode, and the state variables and disturbances are subject to inequality constraints. The horizon estimation approach addressed the constrained state estimation problem, and the Bayesian network technique solved the stochastic jump problem. The moving horizon state estimator designed in this paper can produce the constrained state estimates with a lower error covariance than under the unconstrained counterpart. This new estimation method is used in the design of the restricted state estimator for two practical applications.     

A neural approach for control of nonlinear systems with feedback linearization.

Several schemes for feedback linearization using neural networks have been investigated and compared. Then an approach to design a neurocontroller in the sense of feedback linearization is introduced. The contents include: (1) full input-output linearization when a system has relative degree n; (2) partial input-output linearization when a system has relative degree r (r相似文献   

State estimation scheme for nonlinear dynamical systems based on the stochastic approximation

An algorithm for the state estimation of multivariable nonlinear dynamic systems with noisy nonlinear observation systems is investigated on the basis of stochastic approximation procedure.Using an extended version of Dvoretzky's theorem, we derive a sufficient condition that estimation error converges to zero, both in the mean square and with probability one for noise-free multivariable dynamical systems. We then show that our estimation procedure makes the estimation error bounded in the mean square norm for noisy dynamical systems. Some numerical examples are presented for the illustration of the approach mentioned above.     

A neural state estimator with bounded errors for nonlinear systems

A neural state estimator is described, acting on discrete-time nonlinear systems with noisy measurement channels. A sliding-window quadratic estimation cost function is considered and the measurement noise is assumed to be additive. No probabilistic assumptions are made on the measurement noise nor on the initial state. Novel theoretical convergence results are developed for the error bounds of both the optimal and the neural approximate estimators. To ensure the convergence properties of the neural estimator, a minimax tuning technique is used. The approximate estimator can be designed offline in such a way as to enable it to process on line any possible measure pattern almost instantly     

Parity Relation Based Fault Estimation for Nonlinear Systems： An LMI Approach

This paper proposes a parity relation based fault estimation for a class of nonlinear systems which can be modelled by Takagi-Sugeno （TS） fuzzy models. The design of a parity relation based residual generator is formulated in terms of a family of linear matrix inequalities （LMIs）. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations

State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. We propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.