Norm Of State Vector Research Articles

Person Following from a Nonholonomic Mobile Robot with Ultimately Bounded Tracking Error

Abstract In robotics, following depicts the servoing of the relative situation of a robot w.r.t. a moving person. This property may be hard to achieve, especially when the estimation of the person ego-motion is weak (e.g., due to limited prior knowledge or computational resources). This paper introduces a nonholomic mobile robot controller, which ensures an intuitive and safe behavior through an insightful robot-centered problem statement. Under realistic bounded-error readings of hidden constant person velocities, ultimate boundedness of the state vector norm can be ensured in the neighborhood of its equilibrium.

Adaptive control for a class of nonlinear chaotic systems with quantized input delays

This paper proposes adaptive prediction-based control design for nonlinear chaotic systems in the presence of input quantization with actuator delay. A class of sector-bounded quantizer, namely the hysteresis quantizer, has been used to quantize the control signal. Adaptive scheme is utilized to estimate unknown parameters of the nonlinear chaotic system. A new prediction vector is introduced to compensate actuator delay for nonlinear systems with unknown parameters. The proposed controller does not require the restrictive conditions for quantized parameters in contrast to some existing control schemes for systems with input quantization. By error analysis, it is insured that the upper bound of the state vector norm is limited. Moreover, a maximum allowable upper bound for actuator time-delay is achieved and is guaranteed that for any input delay less than this value, the closed-loop system is stable. To show the efficiency of the proposed method, it is applied to brushless DC motor and Chua’s circuit with delayed hysteresis input and compared to the existing results in the literature. Simulation results show that the proposed method is able to compensate actuator time-delay with hysteresis quantized input for a class of nonlinear systems having unknown parameters. The robustness and efficiency of the suggested approach are illustrated by comparative simulation results.

Adaptive neural-based control for non-strict feedback systems with full-state constraints and unmodeled dynamics

In this paper, an adaptive neural network controller is designed for non-strict feedback systems with full-state constraints. According to practical applications, both input saturation and unmodeled dynamics are also taken into account. By using a logarithm nonlinear mapping, non-strict feedback systems with full-state constraints can be converted to unconstrained ones, which may result in some exponential terms. Here, a new variable separation method is proposed based on Taylor’s formula to cope with the exponential terms and non-strict structure. Then, the relationship between the norm of state vector and error functions is established. A hyperbolic tangent function and a dynamic signal are introduced to deal with input saturation and unmodeled dynamics, respectively. It is proved that all signals of the closed-loop system are uniformly ultimately bounded and the requirement of full-state constraints is satisfied. Two illustrative examples are provided to demonstrate the effectiveness of the presented method.

Application of adaptive sliding mode control for nonlinear systems with unknown polynomial bounded uncertainties

In this paper, we discuss the application of a novel switching integral-exponential-adaptation-law-based adaptive sliding mode control design for a wide class of nonlinear systems with unknown polynomial bounds on the uncertainty norm. A robust finite time convergence, i.e. finite stability, is obtained with low chatter on control actions and a fast-transient performance for adaptive sliding mode control handling the multi-input multi-output nonlinear systems with uncertainties of amplitudes bounded within unknown polynomials in the state vector norm. The exponential term of the proposed adaptation law targets the reduction of the chatter levels of the sliding mode by significantly reducing the gain overestimation while simultaneously suppressing the overshoot by speeding up the system response to the uncertainties. It also prevents the instability issues which encounters the classic integral-gain-law-based adaptive sliding mode control when underestimating its initial gain or gain rate parameter. A simple example illustrates the motivation and feasibility of the proposed adaptive sliding mode control. The applications on a nonlinear mass–spring system and on a two degree of freedom electromechanical rotative plant demonstrate the effectiveness of the proposed design.

Theoretical and numerical issues concerning temporal stabilisability and detectability

Motivated by the design of perturbation (output) feedback controllers for nonlinear systems, temporal system properties have been developed by the authors, for time-varying linear continuous-time systems. In particular temporal controllability/reachability, temporal stabilisability, temporal reconstructability/observability and temporal detectability. As opposed to their ordinary counterparts, these temporal properties identify the temporal loss of stabilisability and detectability that may occur for time-varying linear continuous-time systems obtained e.g. by linearising around state and control trajectories of a non-linear system. One contribution of this paper is to show that temporal stabilisability and temporal detectability require a measure of state decay that cannot be independent of the state representation and state vector norm. This raises the issue of how to select the state representation or norm. The second contribution of this paper is to deal with this selection. Thirdly this paper presents two new, alternative ways to compute temporal stabilisability and detectability and their associated measures. They are compared with computations proposed earlier that rely on LQ control. Finally, through simple illustrative examples, numerical aspects concerning computation of temporal stabilisability and detectability and their associated measures are investigated.

Robust Stability and Synthesis of Nonlinear Discrete Control Systems under Uncertainty

With the use of Lyapunov functions chosen as the norm of state vector, we obtain the robust stability sufficient conditions for a wide class of nonlinear, and generally nonstationary, discrete-time control systems with the given set-valued parameter estimates. For a strictly monotone nonlinear function, validation of these conditions is equivalent to solution of a series of combinatorial problem in the state space.Synthesis of robustly stable control systems in a domain is performed on the basis of the obtained sufficient conditions of robust stability.

Improvement in the stability of the BCGM-OR algorithm

The BCGM-OR algorithm was derived on the basis of the results of error analysis of the block orthogonal projection algorithm using the conjugate gradient method. The authors have improved the convergence characteristics of this algorithm significantly under noisy conditions while at the same time reducing the computational load by optimizing the number of iterations for the conjugate gradient method. However, countermeasures are required for unstable operation resulting from variations in the size of the input signal, which is a fundamental limit of the orthogonal projection-type adaptive algorithm in the authors' method. With respect to the learning identification method when the block length of the block orthogonal projection algorithm is 1, the authors have already shown that a guarantee value (the upper limit of the estimated error after convergence) can be obtained by using a method in which the coefficient updating is stopped when the state vector norm becomes smaller than the set threshold value. Based on this method, the authors first stabilize the guarantee value in the BCGM-OR algorithm when performing coefficient update cutoff. They then identify the threshold value used to satisfy the guarantee value and next describe the BCGM-OR algorithm with a guarantee value. Finally, using computer simulations, the authors show good convergence characteristics under noisy conditions for the proposed method, and then confirm that the operational stability is superior particularly with respect to nonstable input signals. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(5): 42–52, 2000

Combining stochastic dynamical state-vector reduction with spontaneous localization.

A linear equation of motion for the state vector is presented, in which an anti-Hermitian Hamiltonian that fluctuates randomly is added to the usual Hamiltonian of the Schr\"odinger equation. It is shown how the resulting theory describes the continuous evolution of a state vector to an ensemble of reduced state vectors while retaining important physical features of the Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)] theory of spontaneous localization, in which the state vector reduction occurs discontinuously. A novel aspect, compared with ordinary quantum theory, is that the state-vector norm changes with time. The squared norm of each state vector is interpreted as being proportional to the probability possessed by that state vector in the ensemble of state vectors. This interpretation is shown to be consistent with the independent Markovian evolution of each state vector.