Augmented Dynamic System Research Articles

A novel smooth quaternion-based attitude tracking control

The fact that two antipodal points in the quaternion characterize the same physical attitude depicts that the design of the global attitude control system is uneasy. This study deals with a smooth quaternion-based attitude tracking control system that is composed of a differential equation known as the augmented dynamical system. The augmented dynamical system plays such an important role that it is possible to conduct a novel perspective on viewing the set containing all possible motions as not a manifold. Therefore, the topological obstruction does not exist. The designed attitude tracking control system has a guarantee of stability in the large within a set containing all possible motions. It is able to avoid the unwinding phenomenon, and it is noise-induced chattering-free since there is no discontinuity. Furthermore, we show that the smooth attitude tracking control system has an integral input-to-state stability (iISS) guarantee in the presence of uncertainties in the moment of inertia and environmental disturbance. Simulations carried out show the effectiveness of the designed attitude tracking control system.

Asynchronous sampled-data dynamic output feedback control for Markovian jump neural networks via a double-mode-dependent Lyapunov functional

This paper discusses the asynchronous switching problem of Markovian jump neural networks (MJNNs) with mode-dependent time delays. Due to the factors such as communication induced phenomena or the incomplete availability of system modes, asynchronous switching between the system mode and the controller mode is a common phenomenon. Therefore considering the mode mismatch phenomenon and the incomplete measurement of system state, we propose an asynchronous dynamic output feedback control (DOFC) law. Unlike the traditional DOFC, the sampled-data strategy is introduced into DOFC to alleviate the burden of the communication network. In light of the sampled-data DOFC, an augmented dynamic system is modeled. To fully employ the mode information of asynchronous switching and to relax the conservativeness of the results, a double-mode-dependent Lyapunov functional is constructed, which depends both on the system modes and the DOFC modes. Then, a less conservative stability condition is obtained to guarantee mean-square asymptotic stability (MSAS) of the augmented system. On the basis of the stability condition, a design algorithm is attained to solve the gain matrices of the asynchronous DOFC. Finally, a simulation example is given to illustrate the validity and superiority of the developed results.

Quaternion feedback attitude control system design based on weighted–[formula omitted]–gain performance

The operation and accomplishment of a satellite's mission depend on its capacity to control its attitude. A rotation matrix parameterization, such as a (unit) quaternion, is frequently used to represent the attitude information needed for attitude control. The quaternion can represent the attitude globally. However, the non-uniqueness property of the quaternion causes difficulty in ensuring stability. A quaternion-based attitude control system with an augmented dynamical system is a class of nonlinear continuous quaternion feedback system to tackle that problem. However, tuning the control law's parameters causes further difficulty. This paper addresses the parameters tuning based on weighted–L2–gain performance in the form of linear matrix inequalities such that the equilibrium set of the attitude control system has the guarantee of the asymptotically stable in the large. The proposed parameter tuning method reduces the setting complexity of the controller parameters that comprise scalars and matrices, i.e., from five to two parameters. It is equivalent to reducing from 37 to 4 parameters' elements. In addition, a disturbance observer is proposed as an additional control torque to overcome angular velocity bias and external disturbance bad effects. We proved that the disturbance estimation error is bounded. Simulations verified the effectiveness of the proposed control systems.

Preview repetitive learning control for islanded microgrids based on equivalent input disturbance approach

Due to the rapid drop in peak dc-link voltage (PDV) caused by environmental changes, as well as the majority of loads being naturally nonlinear, the output voltage of the microgrid inverters is always distorted. To boost the PDV at a low cost and reduce the total harmonic distortion (THD) of output voltage, a strategy is proposed in this paper to synchronously control ac- and dc-sides voltage. A double closed-loop PI controller is used to indirectly control the PDV of Z-source inverter (ZSI). Sinusoidal reference voltage generated by the primary power layer is merged to construct an augmented dynamic system, and an integrated optimal controller on the ac-side is obtained. Preview repetitive control (PRC) and error compensation can improve output voltage tracking accuracy. The state feedback component effectively suppresses the resonance of the filter, lowering the system’s sensitivity to parameter perturbation. Combined with this, the equivalent input disturbance (EID) is used to eliminate the potential interference in microgrids, which can shorten the recovery time of the system. Both simulations and experiments are provided to demonstrate the better performance of the proposed approach in comparison to other different repetitive controllers.

Output Feedback Sliding Mode Control of Markovian Jump Systems and Its Application to Switched Boost Converter

This paper presents a sliding mode dynamic output feedback controller design for Markovian jump systems under a communication network. For the inaccessible states and uncertain parts of Markovian jump systems, a novel integral-type sliding mode output feedback controller combined with system states and dynamic controller states is proposed. An event-triggered mechanism is introduced to reduce network bandwidth and resources requirements. The augmented dynamic system and complete control framework are presented together. The reachability of the novel integral-type sliding mode is proved. Then, based on delay-dependent Lyapunov functions, free-weighting matrices, and a singular value decomposition approach, a less conservative sufficient condition is proposed to ensure exponential stability with a weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {L}_{2}$ </tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{ L}_{\infty}$ </tex-math></inline-formula> disturbance performance. Finally, a numerical and a DC-DC switched boost converter circuit simulations that verify the feasibility and effectiveness of the proposed controller are presented.

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.

Optimal control for quantum metrology via Pontryagin's principle

Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of an optimal control problem and apply Pontryagin's Maximum Principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time. As the quantum Fisher information involves a derivative with respect to the parameter which one wants to estimate, we devise an augmented dynamical system that explicitly includes gradients of the quantum Fisher information. The necessary conditions derived from Pontryagin's Maximum Principle are used to quantify the quality of the numerical solution. The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement.

Output feedback MPC for uncertain delayed system and control of a wind tunnel system

We propose an output feedback model predictive control (MPC) strategy for a class of uncertain systems with state delay and unknown disturbance. In order to handle the state delay, we formulate an augmented dynamic system that includes the delayed states, as well as the original system state, as the augmented state. Then, we utilize a dynamic output feedback control law, which is based on the current estimated state instead of the augmented state, for stabilizing the system. As a result, the order of the controller is much reduced. The benefits of utilizing the reduced order controller are the reduced computational burden and guaranteed recursive feasibility. We apply the proposed approach to a wind tunnel system for regulating the Mach number in the test section to the reference value. The simulation result verifies the effectiveness and practicality of the proposed approach.

Optimal preview repetitive control with application to permanent magnet synchronous motor drive system

In this paper, the problem of optimal preview repetitive control (OPRC) for continuous-time linear systems is proposed. First, an augmented dynamic system including the derivative of the state vector and the output of the basic repetitive controller is constructed by using lift technique. Then, a new performance index is denoted, which transforms the tracking problem into a linear quadratic regulation problem. Based on the optimal control theory, the explicit optimal preview repetitive controller is obtained, which combination of the state feedback, the integral action related to the tracking error, the basic repetitive controller and the preview compensation. Finally, the developed design techniques are applied to permanent magnet synchronous motor (PMSM) speed control problem. The simulation results demonstrate the validity of the proposed method.

Information provision utilizing a dynamic projection system in industrial site assembly

Today, industrial assembly of large equipment is often organized as site assembly. Information is provided on paper or stationary PC-terminals and employees have to walk long distances to receive information. An augmented dynamic projection system allows direct display of work-instructions and interaction on the component. The paper presents the results of an evaluation of a dynamic projection system compared to state-of-the-art information provision. The experiment is carried out using a demonstrator with a CFRP-layup site assembly for aircraft components. The results show that the augmented dynamic projection system brings significant advantages for process improvements and usability compared to PC-terminals.

Optimal Linear Filter for Systems With Random Delay and Packet Dropout Compensations

In this article, the optimal linear filtering problem is investigated for networked control systems with random delays and packet dropouts. The filter may receive the current sensor measurement, the one-step delayed sensor measurement or nothing at each time. When nothing is received by the filter, the predictor of the current sensor measurement which may be delayed or lost is used for compensation. For this measurement compensation model, a new augmented system is established. Based on the established augmented dynamic system, an optimal linear filter dependent on probabilities in the linear minimum sense is developed by an innovation analysis approach. Compared with the filters based on the popular zero-input, hold-input, and modified hold-input compensation strategies, the presented filter has better estimation accuracy. The steady-state filter is also investigated. Simulation examples illustrate the efficiency of the developed filter.

Full Order Observer With Unmatched Constraint: Unknown Parameters Identification

This letter concerns both state estimation and parameters identification for linear system with unmatched unknown parts. It deals with a full order output delayed unknown inputs observer (DUIO), in which, the time delay concept is investigated to define a new augmented dynamic system including delayed state and output vectors. This estimation approach allows to recover the matching condition which can appear in the observer design problem. The resulting observer has been improved, from the restrictive decoupling condition point of view to guarantee the estimation of state and parameters with asymptotic convergence. Finally, a simulation example based on parametric identification is provided to highlight the feasibility of the suggested method.

Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

Actor-Critic Reinforcement Learning Control of Non-Strict Feedback Nonaffine Dynamic Systems

The most focuses of the existing actor-critic reinforcement learning control (ARLC) are on dealing with continuous affine systems or discrete nonaffine systems. In this paper, I propose a new ARLC method for continuous nonaffine dynamic systems subject to unknown dynamics and external disturbances. A new input-to-state stable system is developed to establish an augmented dynamic system, from which I further get a strict-feedback affine model that is convenient for control designing based on a model transformation approach. The Nussbaum function is connected with a fuzzy approximation to devise an actor network whose tracking performance is further enhanced via strengthening signals generated by a fuzzy critic network. The stability of the closed-loop control system is guaranteed by the Lyapunov synthesis. Finally, the comparison simulation results are presented to verify the design.

Faster protein folding using enhanced conformational sampling of molecular dynamics simulation

In this study, we applied swarm particle-like molecular dynamics (SPMD) approach to enhance conformational sampling of replica exchange simulations. In particular, the approach showed significant improvement in sampling efficiency of conformational phase space when combined with replica exchange method (REM) in computer simulation of peptide/protein folding. First we introduce the augmented dynamical system of equations, and demonstrate the stability of the algorithm. Then, we illustrate the approach by using different fully atomistic and coarse-grained model systems, comparing them with the standard replica exchange method. In addition, we applied SPMD simulation to calculate the time correlation functions of the transitions in a two dimensional surface to demonstrate the enhancement of transition path sampling. Our results showed that folded structure can be obtained in a shorter simulation time using the new method when compared with non-augmented dynamical system. Typically, in less than 0.5 ns using replica exchange runs assuming that native folded structure is known and within simulation time scale of 40 ns in the case of blind structure prediction. Furthermore, the root mean square deviations from the reference structures were less than 2Å. To demonstrate the performance of new method, we also implemented three simulation protocols using CHARMM software. Comparisons are also performed with standard targeted molecular dynamics simulation method.

Nonautonomous analysis of steady Korteweg–de Vries waves under nonlocalised forcing

Recently developed nonautonomous dynamical systems theory is applied to quantify the effect of bottom topography variation on steady surface waves governed by the Korteweg–de Vries (KdV) equation. Arbitrary (but small) nonlocalised bottom topographies are amenable to this method. Two classes of free surface solutions–hyperbolic and homoclinic solutions of the associated augmented dynamical system–are characterised. The first of these corresponds to near-uniform free-surface flows for which explicit formulæ are developed for a range of topographies. The second corresponds to solitary waves on the free surface, and a method for determining their number is developed. Formulæ for the shape of these solitary waves are also obtained. Theoretical free-surface profiles are verified using numerical KdV solutions, and excellent agreement is obtained.

A novel Lie-group theory and complexity of nonlinear dynamical systems

The complexity of a dynamical system ẋ=f(x,t) is originated from the nonlinear dependence of f on x. We develop a full Lorentz type Lie-group for the augmented dynamical system in the Minkowski space. Depending on a signum function Sign≔sign(‖f‖2‖x‖2-2(f·x)2)=-sign(cos2θ), where θ is the intersection angle between x and f, we can derive a group-preserving scheme based on SOo(n,1), which has two branches: compact one and non-compact one. The barcode to show the complexity of nonlinear dynamical systems is obtained by plotting the value of Sign with respect to time. The Rössler equation possesses the most elementary chaotic mechanisms of stretching and folding, which is useful to validate the present theory of nonlinear dynamical system. Analyzing the barcode, we can point out the bifurcation of subharmonic motions and the chaotic range in the parameter space. The bifurcation diagram of the percentage of the first set of dis-connectivity A1-≔{sign(cosθ)=+1andsign(cos2θ)=+1} with respect to the amplitude of harmonic loading leads to a finer structure of devil staircase for the ship rolling oscillator, and the cascade of subharmonic motions to chaos for the Duffing oscillator.

Approximation of the pareto optimal set for multiobjective optimal control problems using viability kernels

This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solu- tion of a multiobjective dynamic programming equation. The epigraph of this approximate set-valued return function equals to the finite discrete viability kernel resulting from the convergent numerical ap- proximation of the viability kernel proposed in (P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre. Birkhauser, Boston (1999) 177-247. P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre, Set-Valued Analysis 8 (2000) 111-126). As a result, the epigraph of the approximate set-valued return function con- verges to the epigraph of V. The approximate set-valued return function finally provides the proposed numerical approximation of the Pareto optimal set for every initial time and state. Several numerical examples illustrate our approach. Mathematics Subject Classification. 49M2, 49L20, 54C60, 90C29.

Robust Synchronization of a Class of Nonlinear Systems: Applications to Chaotic Coupled Electromechanical Systems

This article treats the robust synchronization problem of a class of nonlinear systems from a control theoretical point of view. Because of the tremendous complexity of nonlinear systems, the problem is restricted to chaotic electromechanical devices. The results are discussed in the context of complete synchronization. A new dynamic output feedback is applied to perform synchronization in spite of master/slave mismatches. The main idea is to construct an augmented dynamical system from the synchronization error system, which is itself uncertain. The advantage of this method over the existing results is that the synchronization time is explicitly computed. Numerical simulations are provided to verify the operation of the proposed algorithm.

Unstable patterns and robust synchronization in a model of motor pathway in birdsong

This paper investigates the fundamental dynamical mechanism responsible for transition to chaos in periodically modulated Duffing–Van der Pol oscillator. It is shown that a modulationally unstable pattern appears into an initially stable motionless state. A further spatiotemporal transition occurs with a sharp interface from the selected stable pattern to a stabilized pattern or chaotic state. Also, the synchronization of the chaotic state of the model is investigated. The results are discussed in the context of generalized synchronization. The main idea is to construct an augmented dynamical system from the synchronization error system, which is itself uncertain. The advantage of this method over existing results is that the synchronization time is explicitly computed. Numerical simulations are provided to verify the operation of the proposed algorithm.