Showing papers in "IEEE Transactions on Automatic Control in 2000"
TL;DR: A new approach for generalizing the Kalman filter to nonlinear systems is described, which yields a filter that is more accurate than an extendedKalman filter (EKF) and easier to implement than an EKF or a Gauss second-order filter.
Abstract: This paper describes a new approach for generalizing the Kalman filter to nonlinear systems. A set of samples are used to parametrize the mean and covariance of a (not necessarily Gaussian) probability distribution. The method yields a filter that is more accurate than an extended Kalman filter (EKF) and easier to implement than an EKF or a Gauss second-order filter. Its effectiveness is demonstrated using an example.
3,520 citations
TL;DR: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form and it is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice.
Abstract: A method is proposed for designing controllers with arbitrarily small tracking error for uncertain, mismatched nonlinear systems in the strict feedback form. This method is another "synthetic input technique," similar to backstepping and multiple surface control methods, but with an important addition, /spl tau/-1 low pass filters are included in the design where /spl tau/ is the relative degree of the output to be controlled. It is shown that these low pass filters allow a design where the model is not differentiated, thus ending the complexity arising due to the "explosion of terms" that has made other methods difficult to implement in practice. The backstepping approach, while suffering from the problem of "explosion of terms" guarantees boundedness of tracking errors globally; however, the proposed approach, while being simpler to implement, can only guarantee boundedness of tracking error semiglobally, when the nonlinearities in the system are non-Lipschitz.
1,901 citations
TL;DR: A new control design methodology is proposed, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves, which yields global asymptotic stability.
Abstract: This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear time-invariant feedback, this approach yields global asymptotic stability.
1,533 citations
TL;DR: The systematic formulation of Gaussian filters is presented and efficient and accurate numerical integration of the optimal filter is developed, and the new Gaussian sum filter has a nearly optimal performance.
Abstract: We develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gaussian distributions. A new update rule of weights for Gaussian sum filters is proposed. Our numerical tests demonstrate that new filters significantly improve the extended Kalman filter with no additional cost, and the new Gaussian sum filter has a nearly optimal performance.
1,368 citations
TL;DR: It is proved through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems, and practical numerical tests based on mixed-integer linear programming are proposed.
Abstract: We prove, in a constructive way, the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics, automata, and propositional logic. By focusing our investigation on the former class, we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programming.
678 citations
TL;DR: The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear "H/sup 2/" theory.
Abstract: The notion of input-to-state stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite L/sup 2/ gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that of integral input-to-state stability (iISS), is studied. The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear "H/sup 2/" theory. It allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance. We obtain several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations.
639 citations
TL;DR: In this paper, the authors present a dynamical friction model structure which allows accurate modeling both in the sliding and the presliding regimes, and the transition between these two regimes is accomplished without a switching function.
Abstract: Presents a dynamical friction model structure which allows accurate modeling both in the sliding and the presliding regimes. Transition between these two regimes is accomplished without a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. These last aspects prove essential for modeling presliding friction that is encountered in real physical situations. The model as a whole can also handle the Stribeck effect and stick-slip behavior as has been demonstrated by validation on a KUKA IR 361 robot. In this sense, this model can be considered as more complete in comparison with others found in the literature. The general friction model allows modeling of individual friction systems through the identification of a set of parameters that determine the complete behavior of the system. In this way, the model structure has been used to identify the friction behavior of a linear slide as well as that of the above mentioned KUKA robot. The results of the latter identification have been consequently used for feedforward friction compensation to obtain the most accurate tracking.
605 citations
TL;DR: A robust adaptive control algorithm is developed without constructing a hysteresis inverse, which ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision.
Abstract: Deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation. By exploiting solution properties of the differential equation and combining those properties with adaptive control techniques, a robust adaptive control algorithm is developed without constructing a hysteresis inverse. The new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision. Simulations performed on a nonlinear system illustrate and clarify the approach.
578 citations
TL;DR: This paper examines the operation of a train on a variable grade profile subject to arbitrary speed restrictions to determine a detailed program for traction and brake applications, which minimizes energy consumption in moving the train along a given route for a given time.
Abstract: This paper examines the operation of a train on a variable grade profile subject to arbitrary speed restrictions. The purpose of the study is to determine a detailed program for traction and brake applications, which minimizes energy consumption in moving the train along a given route for a given time. Stated in the form of optimal control, this problem is solved by constructing a numerical algorithm which essentially exploits analytical properties of the optimal solution obtained from the maximum principle analysis. Due to its analytical origin, the algorithm has inherent accuracy and adequate quick-operation that are demonstrated in numerical examples.
524 citations
TL;DR: In this article, a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians was developed, which involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagranian.
Abstract: We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane.
518 citations
TL;DR: It is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy and an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law.
Abstract: The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy.
TL;DR: The control of an underactuated two-link robot called the Pendubot is presented, with a controller for swinging the linkage and raise it to its uppermost unstable equilibrium position based on an energy approach and the passivity properties of the system.
Abstract: This paper presents the control of an underactuated two-link robot called the Pendubot. We propose a controller for swinging the linkage and raise it to its uppermost unstable equilibrium position. The balancing control is based on an energy approach and the passivity properties of the system.
TL;DR: This paper addresses the dynamic output feedback control problem of continuous-time Markovian jump linear systems with an LMI characterization, comprising all dynamical compensators that stabilize the closed-loop system in the mean square sense.
Abstract: This paper addresses the dynamic output feedback control problem of continuous-time Markovian jump linear systems. The fundamental point in the analysis is an LMI characterization, comprising all dynamical compensators that stabilize the closed-loop system in the mean square sense. The H/sub 2/ and H/sub /spl infin//-norm control problems are studied, and the H/sub 2/ and H/sub /spl infin// filtering problems are solved as a by product.
TL;DR: The paper presents a general adaptive SA algorithm that is based on a simple method for estimating the Hessian matrix, while concurrently estimating the primary parameters of interest, based on the "simultaneous perturbation (SP)" idea introduced previously.
Abstract: Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root finding with noisy input information. As with all stochastic search algorithms, there are adjustable algorithm coefficients that must be specified, and that can have a profound effect on algorithm performance. It is known that choosing these coefficients according to an SA analog of the deterministic Newton-Raphson algorithm provides an optimal or near-optimal form of the algorithm. However, directly determining the required Hessian matrix (or Jacobian matrix for root finding) to achieve this algorithm form has often been difficult or impossible in practice. The paper presents a general adaptive SA algorithm that is based on a simple method for estimating the Hessian matrix, while concurrently estimating the primary parameters of interest. The approach applies in both the gradient-free optimization (Kiefer-Wolfowitz) and root-finding/stochastic gradient-based (Robbins-Monro) settings, and is based on the "simultaneous perturbation (SP)" idea introduced previously. The algorithm requires only a small number of loss function or gradient measurements per iteration-independent of the problem dimension-to adaptively estimate the Hessian and parameters of primary interest. Aside from introducing the adaptive SP approach, the paper presents practical implementation guidance, asymptotic theory, and a nontrivial numerical evaluation. Also included is a discussion and numerical analysis comparing the adaptive SP approach with the iterate-averaging approach to accelerated SA.
TL;DR: This work proposes an approach that deploys a fixed state-feedback law but introduces extra degrees of freedom through the use of perturbations on the fixedState-Feedback law to allow for better performance and wider applicability.
Abstract: Predictive constrained control of time-varying and/or uncertain linear systems has been effected through the use of ellipsoidal invariant sets (Kothare et al., 1996). Linear matrix inequalities (LMIs) have been used to design a state-dependent state-feedback law that maintains the state vector inside invariant feasible sets. For the purposes of prediction however, at each time instant, the state feedback law is assumed constant. In addition, due to the large number of LMIs involved, online computation becomes intractable for anything other than small dimensional systems. Here we propose an approach that deploys a fixed state-feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state-feedback law. The problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online. Over and above the very significant reduction in computational cost, the extra degrees of freedom allow for better performance and wider applicability.
TL;DR: An optimal stochastic linear-quadratic control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables, and introduces linear matrix inequalities (LMIs) whose feasibility is shown to be equivalent to the solvability of the SARE.
Abstract: This paper deals with an optimal stochastic linear-quadratic (LQ) control problem in infinite time horizon, where the diffusion term in dynamics depends on both the state and the control variables. In contrast to the deterministic case, we allow the control and state weighting matrices in the cost functional to be indefinite. This leads to an indefinite LQ problem, which may still be well posed due to the deep nature of uncertainty involved. The problem gives rise to a stochastic algebraic Riccati equation (SARE), which is, however, fundamentally different from the classical algebraic Riccati equation as a result of the indefinite nature of the LQ problem. To analyze the SARE, we introduce linear matrix inequalities (LMIs) whose feasibility is shown to be equivalent to the solvability of the SARE. Moreover, we develop a computational approach to the SARE via a semi-definite programming associated with the LMIs. Finally, numerical experiments are reported to illustrate the proposed approach.
TL;DR: In this paper, the robust stochastic stabilizability and robust H/sub /spl infin// disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters are investigated.
Abstract: This paper is concerned with the robust stochastic stabilizability and robust H/sub /spl infin// disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. Sufficient conditions on the existence of a robust stochastic stabilizing and /spl gamma/-suboptimal H/sub /spl infin// state-feedback controller are presented using the Lyapunov functional approach. It is shown that a robust stochastically stabilizing H/sub /spl infin// state-feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities.
TL;DR: The problem of eliminating the chattering effect is presented with reference to a class of uncertain multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.
Abstract: A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)]=0 in the system state space, with s/spl dot/[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s/spl uml/[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.
TL;DR: The technique provides a general procedure for using NNs to determine the preinverse of an unknown right-invertible function and yields tuning algorithms for the weights of the two NNs.
Abstract: A compensation scheme is presented for general nonlinear actuator deadzones of unknown width. The compensator uses two neural networks (NNs), one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path. The compensator NN has a special augmented form containing extra neurons whose activation functions provide a "jump function basis set" for approximating piecewise continuous functions. Rigorous proofs of closed-loop stability for the deadzone compensator are provided and yield tuning algorithms for the weights of the two NNs. The technique provides a general procedure for using NNs to determine the preinverse of an unknown right-invertible function.
TL;DR: It is shown in this work that the implementation of this additional constraint into the online optimization makes it possible to prove strong nominal stability properties of the closed-loop system.
Abstract: This paper addresses the development of stabilizing state and output feedback model predictive control (MPC) algorithms for constrained continuous-time nonlinear systems with discrete observations. Moreover, we propose a nonlinear observer structure for this class of systems and derive sufficient conditions under which this observer provides asymptotically convergent estimates. The MPC scheme proposed consists of a basic finite horizon nonlinear MPC technique with the introduction of an additional state constraint, which has been called a contractive constraint. The resulting MPC scheme has been denoted contractive MPC. This is a Lyapunov-based approach in which a Lyapunov function chosen a priori is decreased, not continuously, but discretely; it is allowed to increase at other times. We show in this work that the implementation of this additional constraint into the online optimization makes it possible to prove strong nominal stability properties of the closed-loop system.
TL;DR: This paper proposes a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria and provides a physical explanation to it.
Abstract: In this paper, we propose a constructive procedure to modify the Hamiltonian function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for nonzero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions can be easily constructed. Interestingly enough, for linear systems the resulting Lyapunov function is the incremental energy; thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are given.
TL;DR: In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type and the thickness of the boundary layer can be reduced to O(T/sup 2/).
Abstract: The use of a discontinuous control law (typically, sign functions) in a sampled-data system will bring about chattering phenomenon in the vicinity of the sliding manifold, leading to a boundary layer with thickness O(T), where T is the sampling period. However, by proper consideration of the sampling phenomenon in the discrete-time sliding mode control design, the thickness of the boundary layer can be reduced to O(T/sup 2/). In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type.
TL;DR: The principal contributions of the paper are the proof of global stability of the overall system and the convergence of the tracking error signal to zero in the deterministic case and theProof of converge of the minimum variance control problem.
Abstract: The adaptive control of a linear time-invariant discrete-time system using multiple models is considered in this paper. Both the deterministic (noise free) case and the stochastic case when random disturbances are present are discussed. Based on the prediction errors of a finite number of fixed and adaptive identification models, a procedure is outlined for switching between a finite number of controllers to improve performance. The principal contributions of the paper are the proof of global stability of the overall system and the convergence of the tracking error signal to zero in the deterministic case and the proof of convergence of the minimum variance control problem. Computer simulation results are included to complement the theoretical results.
TL;DR: This paper solves problems of worst-case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting and shows that the minimax LQG problem will have a solution if and only if a corresponding H/sup /spl infin// control problem has a solution.
Abstract: This paper considers a new class of discrete time stochastic uncertain systems in which the uncertainty is described by a constraint on the relative entropy between a nominal noise distribution and the perturbed noise distribution. This uncertainty description is a natural extension to the case of stochastic uncertain systems, of the sum quadratic constraint uncertainty description. This paper solves problems of worst-case robust performance analysis and output feedback minimax optimal controller synthesis in a general nonlinear setting. Specializing these results to the linear case leads to a minimax linear quadratic Gaussian (LQG) optimal controller. This controller is defined by Riccati difference equations and a Kalman filter-like state equation. The paper also shows that the minimax LQG problem will have a solution if and only if a corresponding H/sup /spl infin// control problem has a solution. A linear example is presented to illustrate the minimax LQG methodology.
TL;DR: A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions, that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant, is presented.
Abstract: A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions, that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant, is presented. The approach is based on the concept of Petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed-loop system. The synthesis technique is based on the concept of admissible constraints. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissible ones. A technique is described for creating a modified Petri net controller that enforces the union of all of these control laws. The method is practical and computationally inexpensive in terms of size, design time, and implementation complexity.
TL;DR: This geometric control theory is offered as one of reading book for you, where by reading, you can open the new world and get the power from the world.
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TL;DR: An iterative procedure of constructing a stabilizing controller using appropriate Lynapunov-Krasovskii functionals is developed and a practical industry process is provided to illustrate the application of the main result.
Abstract: This paper examines the problem of robust stabilization of a class of triangular structural time-delay nonlinear systems. Based on the constructive use of appropriate Lynapunov-Krasovskii functionals, an iterative procedure of constructing a stabilizing controller is developed. A practical industry process is provided to illustrate the application of the main result.
TL;DR: A robust two-stage Kalman filter which is unaffected by the unknown inputs can be readily derived and serves as an alternative to the Kitanidis' (1987) unbiased minimum-variance filter.
Abstract: A method is developed for the state estimation of linear time-varying discrete systems with unknown inputs. By making use of the two-stage Kalman filtering technique and a proposed unknown inputs filtering technique, a robust two-stage Kalman filter which is unaffected by the unknown inputs can be readily derived and serves as an alternative to the Kitanidis' (1987) unbiased minimum-variance filter. The application of this new filter is illustrated by optimal filtering for systems with unknown inputs.
TL;DR: Presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large-scale systems using nonlinear output feedback using a recursive, decentralized, output-feedback design procedure.
Abstract: Presents a solution to the problem of decentralized adaptive asymptotic tracking for a class of large-scale systems using nonlinear output feedback. The proposed constructive approach does not require any matching conditions on the parametric uncertainties nor growth conditions of any kind on the subsystem and interacting output nonlinearities. Any decentralized system in the family may have an unknown, nonzero equilibrium point. Partially decentralized reduced-order filters are presented to recover the unmeasured states. The recursive, decentralized, output-feedback design procedure is illustrated in a practical example of two inverted pendulums on carts without velocity measurements. The effectiveness of the decentralized algorithm is supported by simulation results.
TL;DR: It is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable.
Abstract: This work extends the geometric theory of output regulation to linear distributed parameter systems with bounded input and output operator, in the case when the reference signal and disturbances are generated by a finite dimensional exogenous system. In particular it is shown that the full state feedback and error feedback regulator problems are solvable, under the standard assumptions of stabilizability and detectability, if and only if a pair of regulator equations is solvable. For linear distributed parameter systems this represents an extension of the geometric theory of output regulation developed in Francis (1997) and Isidori and Byrnes (1990). We also provide simple criteria for solvability of the regulator equations based on the eigenvalues of the exosystem and the system transfer function. Examples are given of periodic tracking, set point control, and disturbance attenuation for parabolic systems and periodic tracking for a damped hyperbolic system.