Leader Follower Formation Control for Underwater Transportation Using Multiple Autonomous Underwater Vehicles

The successful ability to conduct underwater transportation using multiple autonomous underwater vehicles (AUVs) is important for the commercial sector to undertake precise underwater installations on large modules, whilst for the military sector it has the added advantage of improved secrecy for clandestine operations. The technical requirements are the stability of the payload and internal collision avoidance while keeping track of the desired trajectory considering the underwater effects. Here, a leader-follower formation control strategy was developed and implemented on the transportation system of AUVs. PID controllers were used for the vehicles and a linear feedback controller for maintaining the formation. A Kalman Filter (KF) was designed to estimate the full state of the leader under disturbance, noise and limited sensor readings. The results demonstrate that though the technical requirements are met, the thrust oscillations under disturbance and noise produce the undesired heading angles.

Constrained regulation problem for continuous-time stochastic systems under state and control constraints

Constrained regulation problem (CRP) for continuous-time stochastic systems is investigated in this article. New existence conditions of linear feedback control law for continuous-time stochastic systems under constraints are proposed. The computation method for solving constrained regulation problem of stochastic systems considered in this article is also presented. Continuous-time stochastic linear systems and stochastic nonlinear systems are focused on, respectively. First, the condition of polyhedral invariance for stochastic systems is established by using the theory of positive invariant set and the principle of comparison. Second, the asymptotic stability conditions in the sense of expectation for two types of stochastic systems are established. Finally, finding the linear feedback controller model and corresponding algorithm of constrained regulation problem for two types of stochastic systems are also proposed by using the obtained condition. The presented model of the stochastic constrained regulation problem in this article is formulated as a linear programming problem, which can be easily implemented from a computational point of view. Our approach establishes a connection between the stochastic constrained regulation problem and positively invariant set theory, as well as provides the possibility of using optimization methodology to find the solution of stochastic constrained regulation problem, which differs from other methods. Numerical examples illustrate the proposed method.

Functional observer-based feedback controller for ball balancing table

The two degree of freedom ball balancing table (BBT) is a well-known didactic tool used to evaluate the effectiveness and performances of many control algorithms for dynamic systems. The present paper proposes to control the ball position of the BBT system via a linear feedback controller based on a functional observer. The parameters of the linear functional observer are determined by applying the direct method which requires neither a Sylvester equation resolution nor canonical transformations. The use of a digital controller has motivated the elaboration of the equations in the discrete time case. In this work, the BBT is tested in real-time to evaluate the proposed controller performances when stabilizing a ball on a reference point. This paper is a continuity of the previous work [12], in which only simulation results have been carried out.

Stability Analysis and Controller Design for Linear Time Periodic Systems Using Normal Forms

The investigation of stability bounds for linear time periodic systems have been performed using various methods in the past. The Normal Forms technique has been predominantly used for analysis of nonlinear equations. In this work, the authors draw comparisons between the Floquet theory and Normal Forms technique for a linear system with time periodic coefficients. Moreover, the authors utilize the Normal Forms technique to transform a linear time periodic system to a time-invariant system by using near identity transformation, similar to the Lyapunov Floquet (L-F) transformation. The authors employ an intuitive state augmentation technique, modal transformation and near identity transformations to enable the application of time independent Normal Forms directly without the use of detuning or book-keeping parameter. This method provides a closed form analytical expression for the state transition matrix with the elements as a function of time. Additionally, stability analysis is performed on the transformed system and the resulting transitions curves are compared with that of numerical simulation results. Furthermore, a linear feedback controller design is discussed based on the stability bounds and the implementation of an effective feedback controller for an unstable case is discussed. The theory is validated and verified using numerical simulations of temporal variation of a simple linear Mathieu equation.

Projection Synchronization of a Class of Complex Chaotic Systems with Both Uncertainty and Disturbance

This paper mainly investigates the projection synchronization of complex chaotic systems with both uncertainty and disturbance. Using the linear feedback method and the uncertainty and disturbance estimation- (UDE-) based control method, the projection synchronization of such systems is realized by two steps. In the first step, a linear feedback controller is designed to control the nominal complex chaotic systems to achieve projection synchronization. An UDE-based controller is proposed to estimate the whole of uncertainty and disturbance in the second step. Finally, numerical simulations verify the feasibility and effectiveness of the control method.

Attitude Optimization Control of Unmanned Helicopter in Coal Mine Using Membrane Computing

Unmanned helicopter for mission inspection has good application value in intelligent coal mining, and attitude control is important. In this paper, membrane computing is introduced to realize attitude optimization control of an unmanned helicopter. First, we give the application scenarios of unmanned helicopters in coal mines. Secondly, we establish a dynamic model of an unmanned helicopter with environmental participation, and the attitude model of the helicopter is deduced based on this model. Further, the cellular membrane system suitable for the attitude model of an unmanned helicopter under the control parameters of environment mapping is constructed, and the cellular membrane controller based on the characteristics and operation rules of the membrane system is designed. The robust performance of the controller is proved theoretically, and by the semiphysical experiments, the performance of trajectory tracking is almost consistent and attitude angle control is less than ±1°, in the range of ±2° by wind disturbance. Compared with the linear feedback controller in the same experimental environment, the performance of the membrane controller is improved by nearly 0.4026 on average. It shows that the cellular membrane controller constructed has good effectiveness and robustness. This will provide a good application value for membrane computing in the field of accurate coal mining.

Controlling Dynamics to Coexisting Periodic Solutions or Equilibrium Points of the n-Scroll Modified Chua’s Circuit

The modified Chua’s circuit, which is first order differentiable, has degree-of-discontinuity [Formula: see text]. It has [Formula: see text] equilibrium points, including two boundary equilibrium points. For them, except boundary equilibrium points, we obtain in theory, conditions under which Hopf bifurcations exist, which implies coexisting periodic solutions. At the same time, we also show that equilibrium points are asymptotically stable when system parameters are within some limits. Furthermore, we theoretically design a linear feedback controller, which will not change the equilibrium points, with appropriate control parameters to control the dynamical behaviors including chaos to these periodic solutions or equilibrium points, and we verify it by numerical simulations.

Exponential Synchronization of Chaotic Xian System Using Linear Feedback Control

In this paper, a new linear feedback controller for synchronization of two identical chaotic systems in a master-slave configuration is presented. This controller requires knowing a priori Lipschitz constant of the nonlinear function of the chaotic system on its attractor. The controller development is based on an algebraic Riccati equation. If the gain matrix and the matrices of Riccati equation are selected in such a way that a unique positive definite solution is obtained for this equation, then, with respect to previous works, a stronger result can be guaranteed here: the exponential convergence to zero of the synchronization error. Additionally, the nonideal case is also studied, that is, when unmodeled dynamics and/or disturbances are present in both master system and slave system. On this new condition, the synchronization error does not converge to zero anymore. However, it is still possible to guarantee the exponential convergence to a bounded zone. Numerical simulation confirms the satisfactory performance of the suggested approach.