Unobservable Subsystems Research Articles

State of charge estimation for lithium-ion batteries with pre-set convergence time based on a comprehensive unobservable model

State of charge (SOC) is a critical metric for assessing the remaining capacity of lithium-ion batteries, while convergence time is an essential indicator for evaluating the performance of SOC estimation. To reduce the convergence time of SOC estimation, a novel strategy has been proposed. Initially, an accurate and comprehensive model is employed for lithium-ion batteries, which includes the nonlinear behavior of the open circuit voltage (OCV) with respect to SOC. However, the linear component of this model is unobservable. Then, the nonlinear relationship between OCV and SOC is approximated using a first-order piecewise fitting function. This approach ensures accuracy while reducing computational complexity compared to non-linearization methods. Next, the unobservable model is decomposed into observable and unobservable subsystems, addressing the challenge of designing observers for unobservable models. Furthermore, a finite time observer is designed based on the observable subsystem, enabling SOC estimation to be achieved within any pre-set convergence time. Finally, theoretical analysis and extensive experimental results validate the feasibility and reliability of the proposed estimation strategy, demonstrating its superiority over traditional methods.

Joint Estimation of Continuous and Discrete States in Randomly Switched Linear Systems With Unobservable Subsystems

Joint Estimation of Continuous and Discrete States in Randomly Switched Linear Systems With Unobservable Subsystems

Mean-square convergent continuous state estimation of randomly switched linear systems with unobservable subsystems and stochastic output noises

This paper studies mean-square (MS) convergent observers for estimating continuous states of randomly switched linear systems (RSLSs) with unobservable subsystems that are subject to stochastic output observation noises. When subsystems are unobservable and switching sequences are random, the classical Kalman–Bucy filters that are applied to observable sub-states are shown to be potentially divergent. It is also shown that unless the switching interval T can be selected to be sufficiently small from the outset, MS convergence may never be achieved, regardless of how the observers for the subsystems are designed. The critical threshold Tmax on T is derived for MS convergent observers to be achievable. Under the condition T<Tmax, this paper introduces design algorithms for subsystem observers to generate a globally MS convergent observer for the entire continuous state. A fundamental design tradeoff between convergence speeds and steady-state estimation errors is analyzed. This paper extends our recent new framework and algorithms for strong convergent observer design in RSLSs by including observation noises, considering multi-output systems, establishing new algorithms for MS convergence, and developing design tradeoff analysis. Examples and a practical case study are presented to illustrate the design procedures, main convergence properties, and error analysis.

Reliable Distributed Integrated Navigation Based on CI during Mars Entry

A reliable distributed covariance intersection (CI) fusion integrated navigation algorithm with information feedback during the Mars atmospheric entry is proposed to meet robust, reliable, and high-precision Mars atmospheric entry navigation strategy. A distributed integrated navigation scheme includes four independent subsystems consisting of an IMU and one radio beacon, but each subsystem is weakly observable under limited Mars entry measurements. The scalar weights are fast obtained by maximizing the information contribution of the corresponding estimate. The distributed framework based upon the CI fusion algorithm is designed by using dynamic information distribution coefficients and information feedback strategy. This distributed fusion approach could meet the lower computation cost and robust and reliable capacity and especially is beneficial to the weakly observable or unobservable subsystems during the Mars entry navigation scheme. Numerical simulations show that the proposed distributed CI fusion integrated navigation algorithm can provide consistent navigation accuracy for the Mars entry vehicle and improve the entry navigation robustness under the weakly observable navigation subsystems.

Finite Control Set Predictive Control and State Estimation of Partially Observable Switching Linear Systems: Application to a Multicellular Converter

This article is about a feedback control and state observation of a class of hybrid systems with some unobservable subsystems. When the system reaches an unobservable configuration, the state observer performance decreases, impacting the overall control performance of the system. For that reason, the majority of the existing controllers uses only measurements of the system’s continuous states when they are equal to the system outputs. To deal with this issue, control trajectories are constrained with respect to -observability criteria using a finite control set predictive control algorithm. The experimentations performed on a multicellular converter are presented and the results obtained show the efficiency of the proposed method.

Single-experiment observability decomposition of discrete-time analytic systems

This paper addresses the single-experiment observability decomposition of discrete-time analytic systems. Unlike the continuous-time case, there exist systems which cannot be decomposed into observable and unobservable subsystems due to the fact that the observable space is not integrable. In this paper, a necessary and sufficient condition for integrability of observable space is given. As a corollary of this condition it is proven that if the system is reversible, the observability decomposition can be always achieved. Moreover, integrability of observable space is also addressed for delta-domain models of non-uniformly sampled systems.

Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

This paper investigates the problem of $$L_1$$ L 1 observer design for positive switched systems. Firstly, a new kind of positive $$L_1$$ L 1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive $$L_1$$ L 1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the $$L_1$$ L 1 -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.

On the Reachability and Observability of Path and Cycle Graphs

In this technical note we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. Specifically, we provide necessary and sufficient conditions, based on simple rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: i) a path graph is reachable (observable) from any single node if and only if the number of nodes of the graph is a power of two,n = 2i ; i ∈N and ii) a cycle is reachable (observable) from any pair of nodes if and only if n is a prime number. For any set of control (observation) nodes, we provide a closed form expression for the (unreachable) unobservable eigenvalues and for the eigenvectors of the (unreachable) unobservable subsystem.

Correlation or decoherence? Quantum beats of atomic inversion in a resonant coherent field

It is shown that the standard reduction procedure (i.e., the calculation of the density matrix of the observable subsystem from the density matrix of a closed quantum system) bringing about decoherence corresponds to the limiting approximation, where the unobservable subsystem is assumed to be in the stationary state with minimum information (infinite temperature). An approximate set of interrelation (correlation) equations for the density matrices of the subsystems is derived. It is shown that the correlation of atom and field can be manifested as the inversion beats of a two-level atom in the known experimental scheme of resonator QED. Experimental observation of such beats would indicate that the observable subsystem (atom) generally conserves information about quantum coherence of the unobservable subsystem (field).

Decomposition of neural systems with nonlinear feedback using stimulus–response data

The need often arises in many modeling studies of physiological systems with feedback, for separate characterization of the feedthrough and feedback components using stimulus–response data from the entire system. For instance, the hippocampal formation consists of multiple feedback connections which are difficult to identify experimentally. This paper investigates the application of adaptive estimation techniques in the context of the Volterra–Wiener approach to decompose unobservable subsystems from the overall feedback system data. Computer simulation studies have demonstrated its effectiveness over the traditional approach which employs nonlinear systems analysis in the frequency domain. This approach can be used to indirectly characterize the unobservable feedback basket cells in the hippocampus utilizing experimental stimulus–response data from dentate granule cells.

Input-output decoupling with stability for Hamiltonian systems

The input-output decoupling problem with stability for Hamiltonian systems is treated using decoupling feedbacks, all of which make the system maximally unobservable. Using the fact that the dynamics of the maximal unobservable subsystem are again Hamiltonian, an easily checked condition for input-output decoupling with (critical) stability is deduced.

Control theoretic approach to inertial navigation systems

In this work, the analysis of inertial navigation systems (INS) is approached from a control theory point of view. Linear error models are presented and discussed and their eigenvalues are computed in several special cases. It is shown that the exact expressions derived for the eigenvalues differ slightly from the commonly used expressions. The observability of INS during initial alignment and calibration at rest is analyzed. A transformation that is based on physical insight is introduced that enables us to determine the unobservable subspace and states rather easily by inspection of the new dynamics matrix. Finally, the relationship between system observability and quality of estima- tion is presented. ever, as will be shown in the sequel, the inclusion of the vertical channel does alter the eigenvalues slightly. In the examination of system observability, we use a straightforward transforma- tion into observable and unobservable subsystems that, in turn, expose the states that hamper the estimation of INS errors during the initial alignment and calibration phase of operation. This approach was adopted successfully in the past by Kor- tum3 who considered the problem of INS platform alignment in which the measurements were the horizontal accelerometer outputs, whereas in the present case the measurements are the INS horizontal velocity components. In addition, the compari- son of this approach to the classical one that is presented in the present paper, as well as the discussion of uniqueness and the relationship between observability and quality of estimation, provide additional insight into the observability issue. It is hoped that the examination of INS as a unified system from a control theory point of view will shed more light on the system and contribute additional insight into the analysis of INS. In the next section, we describe the INS linear error model that will be the investigated plant. In Sec. Ill, we investigate the eigenvalues of INS in various phases of operation, and in Sec. IV, the issues of controllability and observability of the system are discussed. The relation between system observability and the ability to estimate its states during initial alignment is discussed in Sec. V. Finally, in Sec. VI, the conclusions are presented.

Output canonical form for observable and unobservable systems

A method of transforming a system to an output canonical form is presented in the letter. The procedure given is applicable to both observable and unobservable systems. When the system is not observable, the canonical form displays separately the observable and unobservable subsystems.