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In this article, the controllability and observability of a general networked dynamic system (NDS) are reinvestigated. While some computationally efficient conditions have been established in previous works, difficulties arise when a full normal rank condition is not satisfied for some subsystems. To address this problem, the subsystem connection topology of the NDS is utilized and a sufficient and necessary condition is derived for its controllability and observability in this article. It is observed that the effects of the transmission zeros and the uncontrollable/unobservable modes of subsystems should be eliminated by subsystem connections to guarantee the controllability/observability of an NDS. Moreover, a sufficient condition and a necessary condition are provided for constructing controllable/observable NDSs in the view of subsystem connection topology and subsystem internal input/output signal, respectively. Finally, the sensor placement of a mechanical system is discussed, which shows the effectiveness of our results.

This paper investigates the problem of fault estimation and fault tolerant control for a class of T-S fuzzy stochastic singular systems. An integral-type sliding surface based augmented singular sliding mode observer, which is applicable to both dual normalized and non-dual normalized singular systems, is constructed. It is shown that the restrictive rank condition and the equality constraint can be removed. Then a sufficient condition in terms of linear matrix inequalities is developed to guarantee the asymptotically mean square admissibility of the closed-loop systems such that the fault can be estimated and the open-loop system can be stabilized. Moreover, a new adaptive sliding mode controller is designed such that the reachability condition can be guaranteed. Finally, two examples are presented to verify the effectiveness of the proposed method.

This article studies the controllability degree via analyzing the condition number of Gramian matrix. Our aim is to explore how the network characteristics affect the controllability degree. Specifically, we prove that a large time parameter would worsen the controllability degree. The time parameter could be understood as the network coupling strength. For directed path networks, we derive how edge weights and time parameter jointly determine the best controllability degree. Furthermore, we prove that either adding a new edge or enhancing an existing edge weight appropriately would worsen the controllability degree. Moreover, through the numerical simulation of external inputs deployment, we find a significant statistical relationship between the controllability index and the controllability degree. In this article, the Gramian matrix reveals the importance of network characteristics that cannot be captured by classic Kalman rank condition or Popov–Belevitch–Hautus (PBH) test.

This paper focuses on fault detection and isolation (FDI) for a network of discrete-time multi-agent systems (MASs) with disturbances, in which a bank of finite-frequency H − / H ∞ unknown input observers (UIOs) are constructed. To detect the fault in one agent, the unknown input consisting of faults in the other agents and disturbances in the whole system can be partitioned into two parts, the decoupled part and the non-decoupled part, which avoids the constraint of the strict rank condition of UIO. To make the generated residual sensitive to the corresponding fault while robust against the non-decoupled unknown input, a finite-frequency H − / H ∞ UIO is proposed, of which the design conditions are transformed into a set of linear matrix inequalities (LMIs). A numerical simulation is conducted to illustrate the effectiveness of the proposed method.

This article proposes various sufficient controllability criteria for a class of networked higher dimensional systems under the influence of impulses exhibited by their state functions. The conditions obtained are characterised in terms of impulse matrices, inner coupling matrix, network topology and the system matrices. It is demonstrated that Kalman’s rank condition and Popov–Belevitch–Hautus (PBH)-rank condition are just sufficient conditions for the controllability of these systems, but not necessary unlike as that of the networked systems without impulses. Various numerical examples are provided to validate the theoretical results. Further, the control function and controlled trajectory are plotted for the systems considered, that helps to estimate the cost of controller.

The Liquid Composite Molding is a processing technique has the capability of manufacturing polymer composites with large size and complex shapes. A good control of process leads to improve the process performance hence the productivity and quality of manufactured parts and that requires knowing all or some process states, but it is often difficult to access these states. However, in many cases, due to cost considerations and physical constraints, the use of sensors is still very limited. In this paper, we overcame the need to use of mechanical sensors by using an observer. This paper proposes an observer for determine the observability for liquid composite molding process. The system observability is analysed by the rank condition, then a nonlinear state observer is designed using a Lyapunov theory and a linear matrix inequalities technique. The observer is formally shown that all variables converge to their true values. The effectiveness of the proposed scheme is demonstrated through computer simulations in the MATLAB/SIMULINK environment.

Lightweight materials in industrial applications have been mostly made of polymer matrix composites. Manufacturing process of composites still requires development to increase quality. Good control of the manufacturing process is very important for reducing injection time and ensuring product quality. Design of a control system is necessary to direct the flow of resin in the desired manner and to prevent the formation of voids during impregnation of resin. So, this paper proposes a derivative controller to achieve real-time and high stabilization precision of the resin transfer molding process. The manufacturing process controllability is analysed by the rank condition and the effectiveness of the proposed control scheme gives best performance to the system controllability.

This paper investigates the construction of interval state observer for Linear Parameter Varying (LPV) systems affected by Unknown Input (UI) and bounded perturbations in both state and measurement equations. The parameter may depend on measurement or other exogenous measurable variables and is bounded in a compact set. The use of Sobolev spaces frame as well as High Order Sliding Mode (HOSM) differentiator enables us to properly access to the successive output derivatives, and thus to obtain an easily attainable rank condition for the decoupling of the UI from the state estimation error. In particular, the proposed rank condition relaxes the classical and widely used one. An interval state observer is provided and its boundedness is proved. Finally, an example illustrates the theoretical contribution.

In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis.

Remotely actuated micro-scale swimming robots have received considerable research attention in recent years due to their promising potential for biomedical applications such as minimally invasive drug delivery. An important requirement for such applications is the ability of the robot to track a reference trajectory. In this work, a micro-robot driven by a torque induced through an applied magnetic field is considered. The spatial and rotational dynamics are formulated in terms of the body-frame torque, which is directly related to the magnetic field in the spatial frame. Controllability of the nonlinear system is then proven using the Lie algebra rank condition. Finally, an iterative linear quadratic tracking algorithm is presented and demonstrated on the system that can track arbitrary paths with both steady and time-varying velocities.

Modally reduced order models are commonly adopted in system inversion. Their observability requires specific attention, since these models only accurately describe the dynamic behavior of the underlying system in a limited frequency range. This paper elaborates a methodology to investigate the observability of modally reduced order models with unknown parameters. The focus is on a particular type of model where the quasi-static contribution of the out-of-band modes is accounted for using so-called dummy modes. The observability test is performed by means of the commonly used Observability Rank Condition (ORC). The proposed methodology is illustrated by multiple examples from structural engineering. It is found that modally reduced order models serve as a valuable alternative for full order models when applied in system inversion. Not only are they computationally much less demanding, but due to their strong link with the underlying full order model, they also allow for the identification of physical parameters, such as mass or stiffness.

Synchronous generators continue to oscillate in multi-machine power systems in many coherent communities, and each community corresponds to the virtual generator. However, coherent communities can vary in response to different activities under different operating conditions. Hence it is necessary to conduct an online analysis however the resulting control actions are based on the system dynamical model. The system models formed using the first principle fail to represent the processes entirely throughout operating circumstances. Therefore a data-driven approach to system modeling is an effective resource for interpreting real-world activities and analyzing its effects in the future. For that, this paper introduces a novel approach for data-driven modeling based on dynamic mode decomposition (DMD) for the coherency identification in a multimachine power system. In order to model the system more efficiently, both steady-state and transient data are considered. An augmented data matrix in the Hankel structure is passed as an input to the DMD algorithm for capturing the behavior of the system accurately. Incorporating the persistency of excitation and Hankel structure in DMD, a rank condition is derived to identify the coherency of generators in post-fault situations. The proposed coherency identification dynamic mode decomposition algorithm is verified and validated on a 22-bus 6-generator system.

International audience; This study addresses the problem of guaranteed state and unknown input (UI) estimation for a class of linearparameter varying systems affected by UIs and other bounded perturbations. The context of interval observer in the cooperativeframework is adopted. Thus, lower and upper bounds of the state and UI are provided. No assumption is made on the UI. Theapproach is based on a rank condition allowing to decouple the UI from the state estimation errors (so that the state estimationis guaranteed, regardless of the variation of the UI). The convergence of the proposed interval observer is studied by Lyapunovtheory and stability conditions are expressed in terms of linear matrix inequalities which ease the design of the gain matrices ofthe observer. Finally, illustrative examples are given for discussion and comparison with respect to the existing results.

In this paper we will analyze the null controllability properties of a linear coupled degenerate parabolic system of n equations when m distributed controls are exerted on the system. First we start with the case when the coupling matrix A is cascade, and then when A is a full matrix, we will prove that the Kalman rank condition on the coupling and the control matrices A and B characterizes the controllability properties of the system.

The problem of state-feedback stabilizability of discrete-time nonlinear systems has been considered in this note. Two assertions have been proved. First, if the system is $N$-step controllable to the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in $N$ steps. Second, if the system is asymptotically controllable to the origin and satisfies the controllability rank condition at the origin, then there is a state feedback control law for which the trajectory of the closed-loop system converges to the origin in finite steps., This work was supported by the Japan Society for the Promotion of Science under Grant-in-Aid for Scientific Research (C) 23560535. This document is the accepted version of the manuscript published in Automatica. Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

In this paper, the relationship between notions of observability for continuous-time nonlinear system related to distinguishability, observability rank condition and K-function has been investigated. It is proved that an autonomous nonlinear system that is observable in both distinguishability and rank condition sense permits an observation window of finite width, and it is possible to construct a K-function related to observability for such system., Comment: This work was supported by the Japan Society for the Promotion of Science under Grant-in-Aid for Scientific Research (C) 23560535. Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

This paper presents the method and characteristic of bearing only localization applying for multiple low-cost autonomous underwater vehicles (AUVs). In the proposed method, each AUV equips sensors which are not always accurate enough to estimate position. The method estimates the positions of the AUVs combining the information of the directions from the AUVs to the acoustic source and sensor values on the AUVs. This paper analyzed the capability of this method using the mathematical model of the system with observability rank condition. The result indicates the system has observability as far as the AUV does not move directly from or to the acoustic source. The position of the AUVs was also estimated using the particle filter. The method succeeded in the particles from diverging. We also observed that the accuracy of the estimation depends on the relative position of the acoustic source from the AUV.

Lie-algebraic controllability analysis is done for the nonlinear dynamical system of DC-DC buck-boost converter. The nonlinear controllability analysis includes Lie Algebra Rank Condition (LARC) and Sussman's theorem on Local Controllability. The theoretical results of this analysis show that the converter is controllable from any equilibrium state for the range of circuit parameters and duty cycle considered in this work. The controllability index has been evaluated and the theoretical results have been validated with the findings of the evaluated controllability index. Buck-boost converter working in continuous current mode (CCM) has been simulated in MATLAB/SIMULINK. It is inferred from the numerical simulation that the system states are controllable for the range of duty cycle, load resistance and circuit parameters considered. The controllability status of DC-DC converter is not affected by the variation in duty cycle and load resistance. The findings of this mathematical analysis and computer simulation based study have substantial importance for understanding the controllability status of the nonlinear dynamical model of DC-DC converters.

In the present study, the technique of Lie algebra has been applied to test controllability of nonlinear dynamical system of DC-DC converter. In order to perform this study, nonlinear controllability conditions comprising of Lie Algebra Rank Condition (LARC) and Sussman's theorem on small time local controllability has been applied. The DC-DC converter considered in this work has been found to be controllable, which is inferred from the plots of system states such as, current flowing through inductor and voltage across capacitor with respect to time. The controllability index has also been computed and the results obtained from nonlinear controllability analysis based on Lie Algebra are matched with the findings based on evaluated controllability index. DC-DC converter working in continuous current mode (CCM) has been simulated in MATLAB/SIMULINK and the system states have been found to be controllable for the different values of duty cycle and input voltage applied for this study. It is found that variation in both duty cycle and input voltage does not influence the controllability of DC-DC converter. The findings of this mathematical analysis and computer simulation based work are significant to understand the controllability status of the nonlinear dynamical systems of power electronic converters.

This paper deals with the stabilization problem for nonlinear control-affine systems with the use of oscillating feedback controls. We assume that the local controllability around the origin is guaranteed by the rank condition with Lie brackets of length up to 3. This class of systems includes, in particular, mathematical models of rotating rigid bodies. We propose an explicit control design scheme with time-varying trigonometric polynomials whose coefficients depend on the state of the system. The above coefficients are computed in terms of the inversion of the matrix appearing in the controllability condition. It is shown that the proposed controllers can be used to solve the stabilization problem by exploiting the Chen-Fliess expansion of solutions of the closed-loop system. We also present results of numerical simulations for controlled Euler's equations and a mathematical model of underwater vehicle to illustrate the efficiency of the obtained controllers., Comment: This is the author's version of the manuscript accepted for publication in the Proceedings of the 12th International Workshop on Robot Motion Control (RoMoCo'19)

Reinforcement learning (RL)-based online approximate optimal control methods applied to deterministic systems typically require a restrictive persistence of excitation (PE) condition for convergence. This paper develops a concurrent learning (CL)-based implementation of model-based RL to solve approximate optimal regulation problems online under a PE-like rank condition. The development is based on the observation that, given a model of the system, RL can be implemented by evaluating the Bellman error at any number of desired points in the state space. In this result, a parametric system model is considered, and a CL-based parameter identifier is developed to compensate for uncertainty in the parameters. Uniformly ultimately bounded regulation of the system states to a neighborhood of the origin, and convergence of the developed policy to a neighborhood of the optimal policy are established using a Lyapunov-based analysis, and simulation results are presented to demonstrate the performance of the developed controller.

Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 – delay-dependent , and 2 – internal-delay independent . The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen׳s inequality, and improved Park׳s inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

The persistence of excitation of signals generated by time-invariant, continuous-time, autonomous linear and nonlinear systems is studied. The notion of persistence of excitation is characterised as a rank condition which is reminiscent of a geometric condition used to study the reachability properties of a control system. The notions and tools introduced are illustrated by means of simple examples and of an application in system identification.

It is challenging to achieve asymptotic estimation of state and actuator faults for systems with unknown perturbations in both the state dynamics and output measurements. To address this, an adaptive sliding mode unknown input observer (ASMUIO) is developed under a mild rank condition of the perturbation distribution matrices. The key idea is to estimate the perturbations simultaneously with the state and faults, which then vanishes the perturbation effects from the estimation error dynamics. Existence conditions and rigorous feasibility proof of the proposed ASMUIO are given. A simulation example is provided to demonstrate the design efficacy in comparison with existing approaches.

Neuromodulation plays a vital role in the prevention and treatment of neurological and psychiatric disorders. Neuromodulation’s feasibility is a long-standing issue because it provides the necessity for neuromodulation to realize the desired purpose. A controllability analysis of neural dynamics is necessary to ensure neuromodulation’s feasibility. Here, we present such a theoretical method by using the concept of controllability from the control theory that neuromodulation’s feasibility can be studied smoothly. Firstly, networks of multiple coupled neural populations with different topologies are established to mathematically model complicated neural dynamics. Secondly, an analytical method composed of a linearization method, the Kalman controllable rank condition and a controllability index is applied to analyze the controllability of the established network models. Finally, the relationship between network dynamics or topological characteristic parameters and controllability is studied by using the analytical method. The proposed method provides a new idea for the study of neuromodulation’s feasibility, and the results are expected to guide us to better modulate neurodynamics by optimizing network dynamics and network topology.

This paper is concerned with a novel control method for a legged-wheel hybrid robot(LWHR). We first derive a contact map from ground reaction forces(GRF) to linear and angular forces on center of mass(CoM). To resolve the lack of rank condition of the contact map due to an existance of reciprocal axis, each of the GRF at the contact points are regulated by a reformed linear invertible contact map while remained forces on the CoM are handled by the kinematic coupling on the conservation of momentum. It would be worthly to remark that there are no singular cases because the reformed contact map has full rank condition kinematically as long as the constraint of each wheels is active. As a result, by this method, we can fully manage all forces on the CoM by which the balance control is accomplished. Finally, we demonstrate the effectiveness of the methods through some simulation results.

Continuum robots offer yet unknown possibilities in the design of modular manipulators with several redundant degrees of freedom. Those designs have various advantages such as an increased dexterity or an implicit fail-safe mechanism. However, established singularity definitions and workspace analysis methods are restricted to non-redundant robots in many cases or become computationally demanding because they scale exponentially with the available degrees of freedom. In this paper, a sufficient condition for forward singularities of redundant, constrained manipulators is given and it is explained why the commonly used rank condition is only a necessary condition. Furthermore, a method to improve efficiency for position workspace analysis is proposed. For an exemplary 6-module manipulator, the required number of samples is reduced by as much as 99.9%.

This chapter develops a data-driven implementation of model-based reinforcement learning to solve approximate optimal control problems online under a persistence of excitation-like rank condition. The development is based on the observation that, given a model of the system, reinforcement learning can be implemented by evaluating the Bellman error at any number of desired points in the state-space. In this result, a parametric system model is considered, and a data-driven parameter identifier is developed to compensate for uncertainty in the parameters. Uniformly ultimately bounded regulation of the system states to a neighborhood of the origin, and convergence of the developed policy to a neighborhood of the optimal policy are established using a Lyapunov-based analysis. Simulation results indicate that the developed controller can be implemented to achieve fast online learning without the addition of ad-hoc probing signals as in Chap. 3. The developed model-based reinforcement learning method is extended to solve trajectory tracking problems for uncertain nonlinear systems, and to generate approximate feedback-Nash equilibrium solutions to N-player nonzero-sum differential games.

Unexpected or time-varying deterministic type load disturbances are often encountered when performing identification tests in practical applications. A bias-eliminated subspace identification method is proposed in this paper by developing an orthogonal projection approach to guarantee consistent estimation on the deterministic part of the plant, in combination with a Maclaurin time series approximation on the output response arising from deterministic type load disturbance. The rank condition for such an orthogonal projection is disclosed in terms of the state-space model structure adopted for identification. Using principal component analysis (PCA), the extended observability matrix and the lower triangular Toeplitz matrix of the state-space model are explicitly derived. Accordingly, the plant state-space matrices can be retrieved from the above matrices through a shift-invariant algorithm. A benchmark example from the literature and an illustrative example of industrial injection molding are used to demonstrate the effectiveness and merit of the proposed identification method.

International audience; In this paper, an interal observer for both state and unknown input estimation is proposed for a Linear Time Invariant (LTI) system. It generalizes previous work done on the subject. Such an observer is constructed under some specific conditions. Among those conditions, a rank condition is needed to ensure the independence between the state estimation and the unknown input. In this paper, former proposed rank condition is relaxed thanks to the use of another one, less restrictive. Moreover, the proposed observer can be applied for systems with the unknown input in both the state and measurement equations. Examples are given to discuss and illustrate the proposed approach.

The controllability of the cascade leader-follower formation system for multi-robots is studied based on the controllability rank condition for general nonlinear system. For the cascade robot formation system, bearing-only unscented Kalman filter (UKF) is used for the state estimation of the leader and the follower robots at all levels, which enables the real-time movement control of the follower robots via input-output feedback control. Simulation results prove the controllability of the cascade robot formation system.

International audience; In this article, we give a necessary and sufficient condition of Kalman type for the indirect controllability of systems of groups of linear operators, under some " regularity and locality " conditions on the control operator that will be made precise later and fits very well the case of distributed controls. Moreover, in the case of first order in time systems, when the Kalman rank condition is not satisfied, we characterize exactly the initial conditions that can be controlled. Some applications to the control of systems of Schrödinger or wave equations are provided. The main tool used here is the fictitious control method coupled with the proof of an algebraic solvability property for some related underdetermined system and some regularity results.

This paper is devoted to the motion planning problem for control-affine systems by using trigonometric polynomials as control functions. The class of systems under consideration satisfies the controllability rank condition with the Lie brackets up to the second order. The approach proposed here allows to reduce a point-to-point control problem to solving a system of algebraic equations. The local solvability of that system is proved, and formulas for the parameters of control functions are presented. Our local and global control design schemes are illustrated by several examples.

This paper studies the approximate and null controllability for impulse controlled systems of heat equations coupled by a pair ( A , B ) of constant matrices. We present a necessary and sufficient condition for the approximate controllability, which is exactly Kalman's controllability rank condition of ( A , B ) . We prove that when such a system is approximately controllable, the approximate controllability over an interval [ 0 , T ] can be realized by adding controls at arbitrary q ( A , B ) different control instants 0 τ 1 τ 2 ⋯ τ q ( A , B ) T , provided that τ q ( A , B ) − τ 1 d A , where d A ≜ min ⁡ { π / | Im λ | : λ ∈ σ ( A ) } and q ( A , B ) ≤ n . We also show that in general, such systems are not null controllable.

The persistence of excitation condition for sequences generated by time-invariant, discrete-time, autonomous linear and nonlinear systems is studied. A rank condition is shown to be equivalent to the persistence of excitation of sequences generated by the class of systems considered, consistently with the results established by the authors for the continuous-time case. The condition is geometric in nature and can be checked a priori for a Poisson stable system, that is, without knowing explicitly the state trajectories of the system. The significance of the ideas and tools presented is illustrated by means of simple examples.

We propose a new observer form based on Koopman operator theoretic framework for input-output nonlinear systems with control affine inputs. Based on this observer form, we describe an observer synthesis framework which exploits estimation techniques developed for Lipschitz systems and bilinear systems. We also formulate nonlinear observability rank condition in terms of the Koopman observer form, and numerically illustrate the benefits of the proposed framework.

Based on the nonlinear controllability theory, this paper analyzes the attitude controllability for an underactuated spacecraft using two or one thrusters in sequence. In order to provide a preconditional guide on designing the control law for the underactuated attitude control system in the actual case, the underactuated spacecraft with respect to the orbit frame is investigated in the presence of periodical oscillation disturbance. First, attitude dynamic model was established for an underactuated spacecraft actuated by three thrusters, one or two of which has failed separately, and the special orthogonal group (SO(3)) is deployed to describe the attitude motions. Second, Liouville theorem and Poincare’s recurrence theorem were used to confirm that the drift field is Weakly Positively Poisson Stable (WPPS). Furthermore, the sufficient and necessary condition of controllability was obtained on the basis of Lie Algebra Rank Condition (LARC). Finally, according to the case of two available thrusters, angular velocity stabilization and three-axis attitude stabilization control laws are designed, and proved by Lyapunov stability theory and LaSalle invariant theorem. The analysis and simulation results illustrate the feasibility of the proposed control law.

In this paper, we present an iterative steering algorithm for nonholonomic systems (also called driftless control-affine systems) and we prove its global convergence under the sole assumption that the Lie Algebraic Rank Condition (LARC) holds true everywhere. That algorithm is an extension of the one introduced in Jean et al. (2005) [21] for regular systems. The first novelty here consists in the explicit algebraic construction, starting from the original control system, of a lifted control system which is regular. The second contribution of the paper is an exact motion planning method for nilpotent systems, which makes use of sinusoidal control laws and which is a generalization of the algorithm described in Murray and Sastry (1993) [29] for chained-form systems.

In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear systems and have found applications in the analysis of nonlinear systems. On the other hand, there is no observability criterion for nonlinear systems corresponding to the PBH test. In this study, we generalize the observability PBH test for nonlinear systems using pseudo-linear transformation.

A functional observer design method is presented for a class of multi-input and multi-output nonlinear systems. The existence conditions of a functional observer are obtained by a rank condition and solving a linear matrix inequality. The proposed functional observer can estimate the system state and unknown input simultaneously. Moreover, exact asymptotic convergence of the estimate can be achieved. Through an example, it will be illustrated that the proposed approach can provide a smaller order of observer than that of the conventional approaches, while maintaining satisfactory performances.

A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.

The problem of observability of the family of nonlinear control systems defined on any time scale and parameterised by time instant t 0 is developed. Necessary and sufficient conditions for observability are given. Because time scale is a rich model of time that includes continuous-and discrete-time models as standard cases, the obtained results extend classical observability rank conditions given for continuous-time systems and discrete-time systems.

In this paper, a new adaptive control framework for linear systems in which the matched uncertainty can be linearly parameterized is introduced to guarantee the global exponential stability of reference tracking error and parameter convergence error without requiring restrictive persistent excitation condition. The framework uses time histories of control input and system signals to construct least-squares problem based on recorded data. Then, unique solution to least-squares problem is computed, and assigned as pre-selected value in well-known σ-modification term. Such indirect use of recorded data matrices results in globally exponential convergence of tracking error and parameter convergence error provided that the recorded matrix satisfies the simple rank condition. The proofs are given by Lyapunov stability theorem, and the results are illustrated with simulations.

The purpose of this paper is to investigate the observability of autonomous navigation system of two satellite system using relative position measurements only. The concept of local $k$-order observability is proposed and introduced into analysis of nonlinear system. Necessary and sufficient conditions of local 4-order, 5-order and 6-order observability of the autonomous navigation system are presented and mathematically proved. The relationships between these three conditions as well as the sufficient and necessary condition of satisfying observability rank condition for the autonomous navigation system are given and proved.

This paper considers the analysis and design of asymptotic unknown input observers (UIOs) for a class of two-dimensional (2-D) nonlinear systems. A sufficient condition for the existence of an asymptotic UIO such that the observer estimation error asymptotically converges to zero is first given in terms of a rank condition on the given system matrices. A systematic method is then presented for the design of UIOs using a linear matrix inequality technique. An example is provided to illustrate the effectiveness of the proposed design method.

“The final publication is available at Springer via http://dx.doi.org/10.1007/s10852-012-9212-6" In this paper a class of linear time-varying control systems is considered. The time variation consists of a scalar time-varying coefficient multiplying the state matrix of an otherwise time-invariant system. Under very weak assumptions of this coefficient, we show that the controllability can be assessed by an algebraic rank condition, Kalman canonical decomposition is possible, and we give a method for designing a linear state-feedback controller and Luenberger observer.

For an underactuated spacecraft using only one thruster, the attitude controllability with respect to the orbit frame is studied in the presence of periodical oscillation disturbance, which provides a preconditional guide on designing control law for underactuated attitude control system. Firstly, attitude dynamic model was established for an underactuated spacecraft, and attitude motion was described using the special orthogonal group (SO (3)). Secondly, Liouville theorem was used to confirm that the flow generated by the drift vector of the underactuated attitude control system is volume-preserving. Furthermore, according to Poincare’s recurrence theorem, we draw conclusions that this drift field is weakly positively poisson stable (WPPS). Thirdly, the sufficient and necessary condition of controllability was obtained on the basis of lie algebra rank condition (LARC). Finally, the controllable conditions were analyzed and simulated in different cases of inertia matrix with the installed position of thruster.

This paper is concerned with functional observers for two-dimensional (2D) systems described by the Fornasini–Marchesini local state-space second model. A necessary and sufficient condition is given for the existence of asymptotic functional observers. A more tractable necessary condition for the existence of asymptotic functional observers is also presented, as it helps exclude those 2D systems for which there is no asymptotic functional observer. A constructive design method is then proposed for the design of asymptotic functional observers using a rank condition on the given system matrices and a linear matrix inequality (LMI) technique. Two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method.

The Transverse Function (TF) approach is applied to the control of a nonholonomic three-segments/snake-like wheeled mechanism, similar to the planar low-dimensional version of Hirose's Active Cord Mechanism (ACM) previously studied by the authors with the same control approach, but with two additional internal degrees of freedom (d.o.f.) whose actuation yields more flexible and efficient control solutions. From a theoretical point of view, these complementary d.o.f. modify the Control Lie Algebra of the system so that only first-order Lie brackets of the control vector fields are needed to satisfy the Lie Algebra Rank Condition (LARC). The fact that four independent (angular velocity) control inputs are used also implies for this system the existence of Transverse Functions (TF) defined on the six-dimensional special orthogonal group(4). Several examples of mechanisms whose control involve TF defined on(3) have been pointed out in the past. Beyond the specific control problem addressed here, a motivation for the present study is to illustrate for the first time how functions defined on the larger set(4) can be determined and used for the control of a physical system. This study is complemented with recalls concerning the parametrization of(4) by pairs of isoclinic quaternions and with the derivation of complementary differential calculus relations associated with this parametrization.

We provide a rank condition for weak observability by defining a modified empirical observability Gramian that explicitly incorporates system control. Based on this rank condition, we derive an upper bound on the local unobservability index of the system that guarantees weak observability. We also show a connection between the Fisher information matrix and the control explicit empirical observability Gramian. The utility of the control explicit Gramian is demonstrated in examples.