Constrained State Space Research Articles

Iterativno upravljanje učenjem u ograničenom prostoru stanja robotskog manipulatora sa 3 stepena slobode

In this paper, the trajectory tracking problem of a nonlinear robotic system with 3DOFs under the control signal obtained through nonlinearly constrained state spaceIterative Learning Control (ILC) methods is considered. The focus of this paper is the analysis of different control system parameters on the convergence rate of two constrained state space ILCalgorithms: Bounded Error Algorithm (BEAILC) and Constrained Output algorithm (COILC), as well as the comparison between these two algorithms through simulations. The obtained results have shown that COILC algorithm converges faster than BEAILC algorithm when compared with the same learning and feedback parameters, due to lower trajectory restrictions. Also, it has been shown that an increase in feedback gains can decrease the number of iteration terminations during the learning process, thus allowing for more of the trajectory error information to be learned from during the single iteration. Moreover, simulations have shown that the decrease in learning parameter values will increase the number of iterations required to obtain the desired tracking accuracy.

State Space Constrained Iterative Learning Control for Robotic Manipulators

AbstractReal‐life work operations of industrial robotic manipulators are performed within a constrained state space. Such operations most often require accurate planning and tracking a desired trajectory, where all the characteristics of the dynamic model are taken into consideration. This paper presents a general method and an efficient computational procedure for path planning with respect to state space constraints. Given a dynamic model of a robotic manipulator, the proposed solution takes into consideration the influence of all imprecisely measured model parameters, making use of iterative learning control (ILC). A major advantage of this solution is that it resolves the well‐known problem of interrupting the learning procedure due to a high transient tracking error or when the desired trajectory is planned closely to the state space boundaries. The numerical procedure elaborated here computes the robot arm motion to accurately track a desired trajectory in a constrained state space taking into consideration all the dynamic characteristics that influence the motion. Simulation results with a typical industrial robot arm demonstrate the robustness of the numerical procedure. In particular, the results extend the applicability of ILC in robot motion control and provide a means for improving the overall trajectory tracking performance of most robotic systems.

Dynamic modelling of a quadratic DC/DC single-switch boost converter

This manuscript proposes the analysis of a Quadratic Boost Converter (QBC) transformer-less single switch typology. The state space average dynamic model and a constrained state space average model taking into account the mono-directional components of the converter (diodes, switches) have been analyzed. The static gain expression taking into consideration the parasitic elements of the converter and the small-signal transfer function of the QBC typology under study has been obtained. A sensitivity analysis has shown a high variation of the gain versus duty-cycle and of the derivative gain versus parasitic parameters of the converter in the range of the duty-cycle from 0.6 to 0.8 which is range of interest for this kind of converter. The small signal model and the static gain function have been used for a closed loop configuration with a feed-forward action in which the structure of the controller is a simple integrator with reference to a practical case study (300W prototype).

A constrained state space approach for estimating firm efficiency

In this study a panel data state space approach is used to estimate efficiencies of productive units where the states are required to lie in a closed convex constraint set. The constraints are imposed by using oblique projections of state variables onto the constraint set. This approach provides a flexible approximation that can capture the time-varying pattern of firm specific efficiency.

Robust Adaptive Neural Tracking Control for a Class of Perturbed Uncertain Nonlinear Systems With State Constraints

In this paper, we deal with the problem of tracking control for a class of uncertain nonlinear systems in strict-feedback form subject to completely unknown system nonlinearities, hard constraints on full states, and unknown time-varying bounded disturbances. Integral barrier Lyapunov functionals are constructed to handle the unknown affine control gains ( $ {g(\cdot )}$ ) with state constraints simultaneously. This removes the need on the knowledge of control gains for control design and avoids the conservative step of transforming original state constraints into new bounds on tracking errors. Neural networks (NNs) are used to approximate the unknown continuous packaged functions. To enhance the robustness, adapting parameters are developed to compensate the unknown bounds on NNs approximations and external disturbances. Design parameters-dependent feasibility conditions are formulated as sufficient conditions for the existence of feasible design parameters to guarantee the state constraints, and an offline constrained optimization step is proposed to obtain the optimal design parameters prior to the implementation of the proposed control. It is proved that the proposed control can guarantee the semiglobal uniform ultimate boundedness of all signals in closed-loop system, all states are ensured to remain in the predefined constrained state space, and tracking error converges to an adjustable neighborhood of the origin by choosing appropriate design parameters. Simulations are performed to validate the proposed control.

Path Planning under Interface-Based Constraints for Assistive Robotics

We present a heuristic-based search method for path planning in shared human-robot control scenarios in which the robot should adhere to specific motion constraints imposed by the human's control interface. This approach to path planning gives special consideration to kinematic and dynamic constraints introduced to reconcile discrepancies between the control space of the user and the control space of the robot. The resulting paths more closely mirror paths produced by users of the same interface; which is helpful, for example, when inferring human intent or for control sharing. Our first insight is to develop a hierarchical finite state machine describing the constrained state space, state transitions and associated costs. We then use this definition to embed the constraints of the interface into our heuristic planning algorithm, named C*, with simple modifications to the A*/D* family of graph search algorithms. This approach allows us to maintain powerful theoretical guarantees such as complexity and completeness. In this paper, we ground our augmented path planning algorithm with an implementation on a robotic wheelchair system and a Sip-and-Puff interface. We demonstrate that the new approach produces paths and control signals that more closely resemble user-generated data and can easily be incorporated into real hardware systems.

Approximation‐based adaptive control of uncertain non‐linear pure‐feedback systems with full state constraints

This study proposes an adaptive approximation-based control approach for non-linear pure-feedback systems in the presence of full state constraints. Completely non-affine non-linear functions are considered and assumed to be unknown. The dynamic surface design based on integral barrier Lyapunov functionals is provided to achieve both the desired tracking performance and the constraints satisfaction, in consideration of the full-state-constrained non-affine non-linearities. In this design procedure, simple sufficient conditions for choosing control gains, which can be checked off-line, are established to guarantee the feasibility of the controller. The function approximation technique is employed to estimate unknown non-linearities induced from the controller design procedure where the adaptive laws using the projection operator are designed to ensure the boundedness of the function approximators in the feasibility conditions. It is shown that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin while all state variables always remain in the constrained state space.

Adaptive Neural Network Control of Uncertain State-Constrained Nonlinear Systems

In this paper, an adaptive neural network control scheme is developed for a class of uncertain nonlinear systems in strict-feedback form subject to the constraints on the full states and unknown system drift dynamics. The Integral Barrier Lyapunov Functionals (iBLF) are utilized to handle the state constraints directly, leading to the relax of the feasibility conditions compared with pure tracking errors based Barrier Lyapunov Function. The radial basis function neural networks (RBFNN) are adopted to approximate and compensate for the unknown continuous packaged functions composed of the unknown system nonlinearities. Novel adapting parameters are constructed to estimate the unknown bounds in neural networks approximation in real time. Based on backstepping design and Lyapunov synthesis, we show that the developed control scheme can guarantee that all signals are semi-globally uniformly ultimately bounded (SGUUB), all states remain in the predefined constrained state space and system output converges to a small neighborhood of the desired trajectory. A practical three-order example is provided to demonstrate the performance of proposed methods.

A direct sampling particle filter from approximate conditional density function supported on constrained state space

Constraints on the state vector must be taken into account in the state estimation problem. Recently, acceptance/rejection and projection methods are proposed in the particle filter framework for constraining the particles. A weighted least squares formulation is used for constraining samples in unscented and ensemble Kalman filters. In this paper, direct sampling from an approximate conditional probability density function (pdf) is proposed. It is obtained by approximating the a priori pdf as a Gaussian. The support of the conditional density is a subset of the intersection of two supports, the 3-sigma bounds of the priori Gaussian and the constrained state space. A direct sampling algorithm is proposed for handling linear and nonlinear equality and inequality constraints. The algorithm uses the constrained mode for nonlinear constraints.

A Robust Null Space Method for Linear Equality Constrained State Estimation

We present a robust null space method for linear equality constrained state space estimation. Exploiting a degeneracy in the estimator statistics, an orthogonal factorization is used to decompose the problem into stochastic and deterministic components, which are then solved separately. The resulting dimension reduction algorithm has enhanced numerical stability, solves the constrained problem completely, and can reduce computational load by reducing the problem size. The new method addresses deficiencies in commonly used pseudo-observation or projection methods, which either do not solve the constrained problem completely or have unstable numerical implementations, due in part to the degeneracy in the estimator statistics. We present a numerical example demonstrating the effectiveness of the new method compared to other current methods.

Modelling & Controlling Monetary and Economic Identities with Constrained State Space Models

Summary The paper presents a method for modelling and controlling time series with identity structures. The approach is presented in the context of monetary targeting where the monetary identity (e.g. reserve money equals net foreign assets plus domestic credit) is modelled using a constrained state space model and next‐period changes in domestic credit (policy variable) are estimated to reach the target level of reserve money. The constrained modelling ensures that aggregation and identity relations among items are dynamically satisfied during estimation, leading to more accurate forecasting and targeting. Applications to Germany, UK and USA show that the constrained state space model provides significant improvements in targeting and forecasting performance over the AR(1) benchmark and the unconstrained model. Reduction in the mean square error of targeting over AR(1) is in the range of 76–95% for the three countries while the gain in targeting efficiency over unconstrained modelling is between 21% and 55%. Beyond monetary targeting, the method has wide application to the dynamic modelling and control of economic and financial time series with identity and aggregation constraints (e.g. balance of payment, national income, purchasing power parity, company balance sheet).

Convergence of Heavy‐tailed Monte Carlo Markov Chain Algorithms

Abstract. In this paper, we use recent results of Jarner & Roberts (Ann. Appl. Probab.,12, 2002, 224) to show polynomial convergence rates of Monte Carlo Markov Chain algorithms with polynomial target distributions, in particular random‐walk Metropolis algorithms, Langevin algorithms and independence samplers. We also use similar methodology to consider polynomial convergence of the Gibbs sampler on a constrained state space. The main result for the random‐walk Metropolis algorithm is that heavy‐tailed proposal distributions lead to higher rates of convergence and thus to qualitatively better algorithms as measured, for instance, by the existence of central limit theorems for higher moments. Thus, the paper gives for the first time a theoretical justification for the common belief that heavy‐tailed proposal distributions improve convergence in the context of random‐walk Metropolis algorithms. Similar results are shown to hold for Langevin algorithms and the independence sampler, while results for the mixing of Gibbs samplers on uniform distributions on constrained spaces are rather different in character.

Constrained state–space system identification with application to structural dynamics

Constrained identification of state–space models representing structural dynamic systems is addressed. Based on physical insight, transfer function constraints are formulated in terms of the state–space parametrization. A simple example shows that a method tailored for this application, which utilizes the non-uniqueness of a state–space model, outperforms the classic sequential quadratic programming method in terms of robustness and convergence properties. The method is also successfully applied to real experimental data of a plane frame structure.

An output feedback precompensator for nonlinear DAE systems with control-dependent state-space

This note considers singular systems of nonlinear differential and algebraic equations (DAEs) whose constrained state space depends on the control inputs. A state-space realization of such systems cannot be derived independently of the controller design. An output feedback precompensator is derived, which results in a modified DAE system whose state-space is invariant under any feedback control law and can be used for output feedback controller synthesis. Its application is illustrated by a nonlinear electrical circuit example.

State-space realizations for output feedback control of linear differential-algebraic-equation systems

This work addresses the derivation of state-space realizations for the output feedback control of linear, high-index differential-algebraic-equation systems that are not controllable at infinity and for which the control inputs appear explicitly in the underlying algebraic constraints. The constrained state space of such systems depends on the control inputs, and thus, a state-space realization cannot be derived independently of the controller design. Motivated by this, initially a dynamic output feedback compensator is designed that yields a modified system for which the algebraic constraints are independent of the new control inputs. For this feedback modified system, a state-space realization is then derived which can be used for output feedback controller synthesis.

Elastic plastic stability of jointed masonry arches

A masonry arch is considered as an assembly of rigid blocks with deformable joints. The joint deformations are characterized by linear hardening plasticity under axial thrust and moment. The activation of four hinges in the arch results in a mechanism. Two types of mechanisms are considered in evaluating a structure: mortar controlled and block controlled. The mortar controlled mechanism is considered by Maier's theory of piecewise linear interacting yield surfaces with linear hardening. The hardening constants and their interactions may be found experimentally. It is found that stable and unstable mechanisms exist, which are predicted by applying first- and second-order optimality conditions to energy functions on a constrained state space. Bounds on the loads activating a mechanism may be determined using bounding theorems similar to the bounding theorems of plasticity. The block controlled behaviour of the system is predicted using Heyman's application of rigid plastic analysis and the bounding theorems of plasticity.

Mathematical Modeling of Constrained Hamiltonian Systems

Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the space of energy variables, which can be rewritten (under a nondegeneracy condition on the internal energy) as an explicit generalized Hamiltonian system on the constrained state space. This is specialized to mechanical systems with kinematic constraints.

On the Hamiltonian formulation of nonholonomic mechanical systems

A simple procedure is provided to write the equations of motion of mechanical systems with constraints as Hamiltonian equations with respect to a “Poisson” bracket on the constrained state space, which does not necessarily satisfy the Jacobi identity. It is shown that the Jacobi identity is satisfied if and only if the constraints are holonomic.

DEVELOPMENT OF A COMPOSITE IDENTIFICATION AND CONTROL FUNCTIONAL FOR A MULTIVARIABLE ADAPTIVE SYSTEM

A structurally constrained discrete state space model is employed as the basis in the development of an identification and control procedure. System excitation is conditioned in accordance with a restricted minimization of a composite cost functional embodying a compromise legitimizing simultaneous identification and control. Alternative scalar measures of the system identified parametric transition matrices are combined with a state quadratic control measure in the composite cost, and an investigation of the effect of a scalar weighting in the functional (offsetting identification with control) considered. Tabular and graphical results are presented covering the likely range of the proposed systems applicability.