Transactions of the Institute of Measurement and Control

Rathore, Sandhya; Sharma, Shambhu N; Bhatt, Dhruvi; Nagarsheth, Shaival

doi: 10.1177/0142331219895711pmid: N/A

Bilinear stochastic differential equations have found applications to model turbulence in autonomous systems as well as switching uncertainty in non-linear dynamic circuits. In signal processing and control literature, bilinear stochastic differential equations are ubiquitous, since they capture non-linear qualitative characteristics of dynamic systems as well as offer closed-form solutions. The novelties of the paper are two: we weave bilinear filtering for the Stratonovich stochasticity. Then this paper unfolds the usefulness of bilinear filtering for switched dynamic systems. First, the Stratonovich stochasticity is embedded into a vector ‘bilinear’ time-varying stochastic differential equations. Then, coupled non-linear filtering equations are achieved. Finally, the non-linear filtering results are applied to an appealing bilinear stochastic Ćuk converter circuit. This paper also encompasses a system of coupled bilinear filtering equations for the vector input Brownian motion case. This paper brings the notions of systems theory, that is, bilinearity, Stratonovich stochasticity, non-linear filtering techniques and switched electrical networks together. Numerical simulation results are presented to demonstrate that the proposed bilinear filter can achieve much better and accurate filtering performance than the conventional Extended Kalman Filter (EKF).

Guo, Jianguo; Su, Yalu; Wang, Xinming; Zhou, Jun

doi: 10.1177/0142331219895928pmid: N/A

A new sliding mode control method based on iterative learning is proposed for the longitudinal dynamics of hypersonic flight vehicles in the presence of wind effects. First, the wind effects are taken into the system by introducing the accessional attack angle, and with output-feedback transformation, the effects of the accessional attack angle and aerodynamic uncertainties are all modelled as lumped disturbances. Then, a novel sliding mode control scheme combined with command filtered technique is designed for the velocity subsystem and the altitude subsystem independently, while iterative learning laws are constructed to estimate the unknown disturbances. Furthermore, the stability and learning convergence of the system are rigorously proven via Lyapunov stability theory. By comparison, simulation results demonstrate that the presented strategy can efficiently achieve high tracking accuracy in spite of wind effects.

Rouamel, Mohamed; Gherbi, Sofiane; Bourahala, Fayçal

doi: 10.1177/0142331219895931pmid: N/A

This paper investigates the robust stability analysis and state feedback controller design of networked control systems (NCSs). A stochastic network-induced delay in given interval with known lower and upper bounds is considered. Therefore, the NCS is modeled as linear system with probabilistic time-varying delay distribution. Then, the Lyapunov-Krasovskii functional (LKF) is formulated using probabilistic informations of both lower and upper bounds of the time-varying network-induced delay, and Wirtinger-based integral inequalities are used to estimate the accuracy of the resulting time derivatives and also to reduce conservatism by introducing some new cross terms. Afterwards, stability condition based on H∞ disturbance attenuation level is expressed in terms of a set of linear matrix inequalities (LMIs), and Finsler’s lemma is used to relax it by adding slack decision variables and decoupling the systems matrices from those of Lyapunov-Krasovskii. This procedure makes the state feedback controller design as simple as a variables change. Finally, a maximum allowable upper bound of the network-induced delay and state feedback controller gains are calculated by resolving the above relaxed LMIs’ convex optimization problem. Practical numerical examples are provided to validate the proposed approach; the results show that the negative effects of the unpredictable network-induced delays are compensated and the stability of NCSs with high disturbance attenuation level is guaranteed. A comparative study with other results in recent researches is also given and the superiority of the proposed method in terms of robustness and conservatism reduction is shown.

Zhang, Shuhua; Chi, Ronghu

doi: 10.1177/0142331219896649pmid: N/A

This work explores a model-free adaptive PID (MFA-PID) control for nonlinear discrete-time systems with rigorous mathematical analysis under a data-driven framework. An improved compact form dynamic linearization (iCFDL) is proposed to transfer the original nonlinear system into an affined linear data model including a nonlinear residual term. Both a time-difference estimator and a gradient parameter estimator are designed to estimate the nonlinear residual uncertainties and the unknown parameters in the iCFDL model. Subsequently, a novel improved CFDL based MFA-PID (iCFDL-MFA-PID) control is proposed by incorporating these two estimators. The results are extended by the use of improved partial format dynamic linearization (iPFDL) and full format dynamic linearization (iFFDL). The theoretical results are shown using contraction mapping principle-based mathematical analysis, as well as simulations.

Duan, Dandan; Liu, Chunsheng; Sun, Jingliang

doi: 10.1177/0142331219897186pmid: N/A

In this paper, the optimal control problem for finite-time missile-target interception systems is posed in a finite-horizon two-player zero-sum (ZS) differential game framework using a periodic event-triggered (PET) scheme. To solve the optimal control problem, a time-varying Hamilton-Jacobi-Issac (HJI) equation and a time-dependent cost function are constructed to deal with finite-horizon constraints, and an event-based periodic adaptive dynamic programming (ADP) algorithm is employed to find the Nash equilibrium solution for the designed HJI equation. Comparing with the traditional continuous event-triggered (ET) scheme, the proposed PET scheme only verifies the event-triggered conditions at periodic sampling instants, which reduces resource consumption in monitoring and excludes the Zeno behavior. A single critic neural network (CNN) is used to implement the proposed event-based optimal control algorithm, which reduces approximate errors bust also simplifies structures. Further, an additional error term is added in the designed weight updating law to such that the terminal constraint is also minimized over time. By resorting to Lyapunov function approach, some sufficient conditions are derived to achieve the uniformly ultimately bounded (UUB) of the ET closed-loop system and the estimation weight error of CNN. Finally, a missile-target interception system is introduced to illustrate the efficiency of the presented methods.

Ashrafifar, Asghar; Jegarkandi, Mohsen Fathi

doi: 10.1177/0142331219897430pmid: N/A

An integrated guidance and control (IGC) is designed in this study for a surface-to-air missile considering burned or broken fin as a fault. The IGC model in the pitch plane is developed with various uncertainties in the presence of fin failure. The considered fault may cause a change in the vehicle’s shape that leads to a change in aerodynamic coefficients and consequently in the model. To identify the new model, aerodynamic coefficients are estimated using an estimator and the result is sent to the controller. Then, an adaptive robust controller is designed using the combination of backstepping and sliding mode scheme to compensate fin failure and changes in the dynamic. The simulation results show the capability of the proposed approach, not only in normal condition but also while a part of the missile’s fin is destroyed.

Sabrine, Bedoui; Anis, Belhadj Brahim; Salwa, Elloumi; Naceur, Benhadj Braiek

doi: 10.1177/0142331219897456pmid: N/A

This paper aims to propose an algebraic method for estimating the stability region for nonlinear discrete systems. The main contribution is the improvement of an existing technique to enlarge the initial stability region in which the asymptotic stability is guaranteed. To deal with the maximization issue, a state feedback controller is proposed to extend the largest estimation of attraction domain of nonlinear polynomial discrete systems. The proposed approach is illustrated and validated on an isothermal stirred tank reactor.

Li, Dongfang; Pan, Zhenhua; Deng, Hongbin

doi: 10.1177/0142331219897992pmid: N/A

In order to study the adaptability of a multi-redundancy and multi-degree-of-freedom snake-like robot to underwater motion, a two-dimensional (2-D) obstacle avoidance control algorithm for a snake-like robot based on immersed boundary-lattice Boltzmann method (IB-LBM) and improved artificial potential field (APF) is proposed in this paper. Firstly, the non-linear flow field model is established under the framework of LBM, and the IB method is introduced to establish a fluid solid coupling of a 2-D soft snake-like robot. Then, the obstacle avoidance of a snake-like robot in a flow field is realized by optimizing the curvature equation of the serpentine curve and eliminating the local minimum in APF method. Finally, the effects by exerted different control parameters on a snake-like robot’s obstacle avoidance capability are analyzed via MATLAB simulation experiment, by which we can find the optimal parameter of the obstacle avoidance and testify the validity of the proposed control algorithm.

Rabiei, Kobra; Ordokhani, Yadollah

doi: 10.1177/0142331219898343pmid: N/A

This paper presents numerical solution for solving the nonlinear one and two-dimensional optimal control problems of arbitrary order. First, we have constructed Boubaker wavelet for the first time and defined a general formulation for its fractional derivative operational matrix. To solve the one-dimensional problem, we have transformed the problems into an optimization one. The similar process together with the Ritz method are applied to find a solution for two-dimensional problems as well. Then, the necessary conditions of optimality result in a system of algebraic equations with unknown coefficients and then control parameters can be simply solved. The error vector is considered to show the convergence of the used approximation in this method. Finally, some illustrative examples are given to demonstrate accuracy and efficiency of the proposed method.

Motahhari, Morteza; Shafiei, Mohammad Hossein

doi: 10.1177/0142331219898634pmid: N/A

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.