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In this paper we consider a time-invariant system of differential equations with an equilibrium. We study the problem of a class of Lyapunov functions allowing to describe an estimation of the domain of attraction (DOA). This work is a development of the results obtained by V. I. Zubov. The solution of the problem is based on the application of the second method of Lyapunov. An example illustrates...
In this paper, a control law for three dimensional trajectory tracking for unmanned aerial vehicles is developed. The control law is based on back stepping method. The parameters of the control law are tuned by genetic algorithm. Simulations show that the effectiveness of the control law and the parameter tuning method. The proposed control law has good performance in the presence of time-varying...
In this paper, we study the containment control problem with general linear dynamics under directed graph by means of centralized event-triggered control strategy. Distributed dynamic centralized event-triggered controller is proposed, which is based on the information of the relative outputs of the neighboring agents, such that the states of the followers can asymptotically converge to convex hull...
In this paper, a nonlinear continuous-time dynamics with input-delay is considered. Assuming the existence of a continuous-time stabilizing strategy in the delay free case, it is shown how the problem can be reformulated in the sampled-data context as an Immersion and Invariance I&I stabilizing one.
In this paper, we seek to establish formal guarantees for whether or not a given human-swarm interaction (HSI) is appropriate for achieving multi-robot tasks. Examples of such tasks include guiding a swarm of robots into a particular geometric configuration. In doing so, we define what it means to impose a HSI control structure on a multi-robot system. Control Lyapunov functions (CLFs) are used to...
Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. As its name implies, EMPC requires the availability of a dynamic model to compute its control actions and such a model may be obtained...
An infinite horizon optimal regulation problem is solved online for a deterministic control-affine nonlinear dynamical system using a state following (StaF) kernel method to approximate the value function. Unlike traditional methods that aim to approximate a function over a large compact set, the StaF kernel method aims to approximate a function in a small neighborhood of a state that travels within...
This paper introduces a class of fixed-time stable dynamical systems with settling time as a explicit parameter, namely the inverse the gain. Those systems are defined as predefined-timed stable dynamical systems. Continuous and discontinuous are cases are presented. A detailed Lyapunov characterization of this class of systems is also shown. Finally, the application to the design of a class of first...
A nonlinear adaptive control algorithm is presented for a model helicopter to achieve the trajectory tracking in the presence of external disturbances. The design process is based on the backstepping technology with the simplified helicopter model. A command filter is utilized to avoid the complicated derivative computation of the virtual control. With the property of the hyperbolic tangent function,...
In many practical applications, stability with respect to part of the system's states is often necessary with finite-time convergence to the equilibrium state of interest. Finite-time partial stability involves dynamical systems whose part of the trajectory converges to an equilibrium state in finite time. Since finite-time convergence implies non-uniqueness of system solutions in backward time, such...
This paper studies the switching control of differential-algebraic equations (DAEs). A specific problem concerned with switched DAEs is that jumps or impulses could be induced by mode switching, which is not well understood in many applications. We aim to find the control strategies that minimize the overall magnitude of undesirable jumps or impulses while rendering the systems achieve the expected...
In this paper we study the stabilization of systems with decentralized controllers, when the stability criterion of interest is “non-overshooting stability”. This criterion is stronger than those which have typically been studied, particularly for decentralized control, and requires that the size of the state is always decreasing. We identify a key property which allows centralized results for this...
This paper introduces a novel control law that dynamically modifies the reference of a pre-compensated nonlinear system so as to ensure the satisfaction of convex constraints. This is done by translating the state space constraints into a constraint on the Lyapunov function which is then limited by modulating the velocity of the applied reference. The main advantage of this approach is that it systematically...
The paper focuses on spatially distributed control systems where the controller sensing and actuation topology is inherited from that of the plant. Specifically, the paper considers distributed systems composed of discrete-time linear parametervarying subsystems interconnected over general graph structures. These distributed systems are subject to a communication latency of one sampling period, where...
In this paper, the problem of stabilization of bilinear control systems is considered. Based on the technique of linear matrix inequalities and quadratic Lyapunov function, the so-called stabilizability ellipsoid is designed, such that the trajectory of the closed-loop system, starting inside the ellipsoid asymptotically tends to zero. The results obtained allow to design an approximation of the stabilizability...
Motion control of UAVs is an interesting problem due to the nonlinear and underactuacted nature of their dynamics. This paper focuses on position and yaw control of a rotary-wing UAV with state and input constraints using an inner-outer loop control structure. The outer loop generates saturated thrust and reference roll and pitch angles, while the inner loop is designed to follow the reference angles...
Lur'e systems are the feedback interconnection of a linear time-invariant system with a memoryless static operator. In this paper, we derive an algorithmic method to incorporate the information given by additional Lyapunov functions in order to enlarge the estimate of the domain of attraction of a Lur'e system. The methodology, limited for simplicity to quadratic Lyapunov functions, relies on the...
A comparative analysis on chattering based on Sliding Mode Controller (SMC) techniques for a single link flexible manipulator is presented in this paper. The proposed controller techniques include i) normal-SMC ii) Quasi-SMC iii) Asymptotic-SMC. These controllers are used in controlling the tip position as well as the tip deflection of the system. Lyapunov stability theory is used to achieve the stability...
A new family of continuous higher order sliding mode algorithm (CHOSMA) for arbitrary relative degree system via continuous control signal is proposed. The convergence conditions for the third order-CHOSMA algorithm is formulated based on homogeneous Lyapunov function. The formula for algorithm of arbitrary order is also suggested. The simulation results are confirmed the efficiency of the proposed...
Robotic navigation applications often require on-line generation of trajectories that respect underactuated non-linear dynamics, while optimizing a cost function that depends only on a low-dimensional workspace (collision avoidance). Approaches to non-linear optimization, such as differential dynamic programming (DDP), suffer from the drawbacks of slow convergence by being limited to stay within the...
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