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This work proposes a control algorithm to stabilize a circular formation of AUVs tracking a time-varying center. We also consider the problem of uniform distribution of all the agents along the circle from two approaches: all-to-all and limited communication. We tackle with this communication constraint using a cooperative control strategy which includes the Laplacian matrix of the communication graph...
A new type of global stability is introduced and its equivalent Lyapunov characterization is presented. The problem of global stability of the compact set composed by all invariant solutions of a nonlinear system (several equilibriums, for instance) is analyzed. Consideration of such set allows us to present global stability properties for multi-stable systems.
In this paper we present the integration of a linear-time-varying model-predictive-control (LTV-MPC), designed to stabilize a vehicle during sudden lane change or excessive speed-entry in curve, with a slip controller that converts the desired longitudinal tire force variation in pressure variation in the brake system. The lateral controller is designed using a three-degrees-of-freedom vehicle model...
We characterize the stability and achievable performance of networked estimation under correlated packet losses described by the Gilbert-Elliot model. For scalar continuous-time linear systems, we derive closed-form expressions for the mean-square distortion of the optimal estimator. The conditions for stable mean square estimation error are equivalent to those obtained previously for stability of...
In this paper, we present some new results on frequency weighted balanced truncation which is a significant improvement on Lin and Chiu's frequency weighted balanced truncation technique. The reduced order models which are guaranteed to be stable in case of double-sided weighting, are obtained by direct truncation. Two sets of simple, elegant and easily calculatable a priori error bounds are also...
In this paper, we extend the interconnection and damping assignment passivity-based control strategy to systems subjected to nonholonomic Pfaffian constraints. The results are applied to stabilize the pitch dynamics of an underactuated mobile inverted pendulum (MIP) robot subjected to nonholonomic constraints arising out of no-slip conditions. A novel feature of this paper is that we reduce the kinetic...
Stability conditions for state-delay systems are derived based on the norm of semigroup, which describes the transition of the internal state. Introducing an exact calculation method of the semigroup norm, the conditions for the internal stability and the marginal stability are characterized by non-singularity of a transcendental function. The conditions depend on the existence of time interval such...
This paper examines the stability of quantum feedback networks. We introduce a novel characterization, in terms of equivalence classes of operators, that may be used to describe open quantum systems. In this characterization, equivalence classes of operators are shown to be elements of a Banach space such that the norm of an operator is analogous to the root mean square expectation value of the operator...
In this paper, we study an extended consensus problem for multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The concept extended consensus means that a combination of each agent's state elements is required to converge to the same vector. For this extended consensus problem, we propose...
This paper presents a new approach to solve a tracking problem for nonlinear minimum-phase systems with a relative degree greater than four by applying nonlinear continuous-time generalized predictive control (NCGPC). In fact, these systems present the particularity to have an unstable closed-loop behavior even if the derived NCGPC control law is applied to them. Indeed, the Routh-Hurwitz criterion...
In this paper we combine an invariant-set approach to fault detection and identification (FDI), recently proposed by the authors, with the virtual actuator approach to controller reconfiguration of Steffen, Lunze and co-authors. The FDI approach is based on the separation of invariant sets that characterise healthy system operation from invariant sets that characterise faulty operation. The derivation...
This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain...
The paper studies how nonlinear PCH Hamiltonian systems are transformed under sampling. We show that Hamiltonian conservation can be preserved under sampling with respect to a modified output mapping. The impact of this result for computing sampled-data stabilizing controllers is illustrated on the basis of an example.
A new criterion is proposed for exact observability of linear stochastic systems. As applications of it, the effects of exact observability due to state/output feedback are investigated. In addition, under the conditions of stability and exact observability, we discuss the property of a set defined by the generalized Lyapunov equations. Finally, with the aid of spectrum technique, we introduce a new...
This paper is concerned with the theory of quasivelocities and its applications to control. The equations of motion of a mechanical system are derived using the Lagrange-d'Alembert principle written in an arbitrary configuration-dependent frame. The structure of the equations of motion written in quasivelocities is utilized in the design of a nonlinear feedback stabilizing controller for an example...
This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensional system is obtained. At each step of the reduction process, a quotient is taken along one-dimensional integral manifolds of the input vector field...
We try to synchronize physical models described by wave equations with nonlinear boundary conditions. These systems are distributed parameter systems in which ideal turbulence, introduced by Sharkovsky et al., occurs. The behavior of such systems can be quite intricate both in time and space. However, by using the d'Alembert's solution, the analysis of the dynamic characteristics can be reduced to...
In this work we investigate the stability of bimodal and bistable (both modes are stable) continuous time linear systems in ??3. Under certain conditions, we first show that all the trajectories which start on the plane separating the two modes are bound to hit the plane again in finite time and go into the other mode. This property yields fixed directions on the separating plane. Eventually, all...
Bi- or even multistable behavior is a recurrent phenomenon in gene regulation networks. These networks have the capacity to operate in two or more distinct modes in a stable manner. In this work, we consider gene regulation networks with known interaction structure but unknown reaction kinetics. Additionally, it is assumed that several distinct operation modes were observed experimentally whereby...
This paper addresses the H?? stability analysis of neutral time-delay systems with multiple commensurate delays including those with poles asymptotic to the imaginary axis. This extends previous work where only the single delay case was considered. Some frequency-domain tests for this kind of stability are proposed.
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