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In this paper, the structural controllability of the systems over $F$ ( $z$ ) is studied using a new mathematical method-matroids. First, a vector matroid is defined over $F$ ( $z$ ). Second, the full rank conditions of $[sI-A\vert B](s\in \wp )$ are derived in terms of the concept related to matroid theory, such as rank, base, and union. Then, the sufficient condition for the linear system and composite system over F(z) to be structurally controllable is obtained. Finally, this paper gives several examples to demonstrate that the married-theoretic approach is simpler than other existing approaches.

The main objective of this article is to present the fixed-point theorem techniques for neutral equation. We consider an unconstrained controllability problem for semi linear stationary dynamical system. In the paper the appropriate hypotheses are presented. In the proof of the main results we use Nussbaum fixed-point theorem and solution of semi linear neutral equation. The main goal of the paper are the sufficient conditions for the relative controllability on the given time interval for studied dynamical system.

In the paper controllability problem of fractional discrete linear systems with constant delays in control is considered. We focus on two cases: firstly, we consider the fractional infinite-dimesional systems, secondly, the fractional positive finite-dimensional systems are studies. The paper contains sufficient and nessesary conditions for controllability for both cases. Finally, illustrative examples are presented.

This paper deals with structured feedback gain design problems for linear time invariant systems. Linear matrix inequality (LMI) conditions with structured LMI variables are derived via stabilizable dilation which is proposed in this paper. Stabilizable dilation is to extend both the state space of the system and the space of the structured feedback gain without loss of stabilizability of the system. Since the number of LMI variables becomes large after its dilation, the LMI problem via stabilizable dilation could be feasible even if the LMI problem without its dilation is infeasible. It is demonstrated through a numerical example. Furthermore, it is shown that, if the problem without dilation is feasible, the problem with dilation is always feasible.

In this paper, an analytic condition is given for determining delayed positive feedback controller for stabilizing an oscillatory system. The $\tau $ -decomposition and $D$ -decomposition methods are employed in deriving this condition. The obtained results are then used to stabilize second order delay systems by a proportional controller. Under-damped and over-damped systems are treated separately, where the Smith-predictor structure is used in the over-damped case to obtain the stability conditions. Illustrative examples are given to show the effectiveness of the proposed approach.

This paper develops a ratio-of-distance (RoD) rigidity theory to study when a framework can be uniquely determined by a set of RoD constraints up to similar transformations (translation, rotation, scaling, and reflection). In particular, a framework is specified by a set of RoD constraints (the RoD of a pair of edges joining a common vertex) instead of distance, bearing, and angle constraints assumed in existing literature. Its relations to three existing rigidity theories (distance, bearing, and angle rigidity theories) are established. The proposed RoD rigidity theory is further applied to the RoD-based similar formation stabilization problem, where the desired formation shape is expressed as a set of RoD constraints. Finally, numerical simulations are presented to illustrate the effectiveness of the theoretical results. Nanyang Technological University National Research Foundation (NRF) Accepted version

This paper exhibits the structure of interval-valued fuzzy linear space (IVFLS) in anti fuzzy setting. Some interesting operations and theorems on interval-valued anti fuzzy linear space (IVAFLS) are provided with suitable examples.

The autonomous maneuverable space net, which consists of a flexible net and several maneuverable units, is a promising solution for the active removal of space debris. A novel dynamics model and a corresponding controller are proposed in this paper to resolve the approach control problem. Given that the net tethers cannot be elongated, interval functions and corresponding constraint forces are exploited to model the unilaterally constrained tethers. The proposed approach dynamics model, which is based on the Hamilton principle, includes distinctive velocity jump phenomena. A dual-loop control scheme with double optimization pseudo-dynamics inversion and sliding mode control is also established. Simulation results validate the feasibility of the proposed control scheme. The net can fly along the expected trajectory without suffering unexpected net deformation or orbital radial movement.

The conditions for state /output non-overshooting measured by the state /output 2-norm of discrete-time switched linear systems are addressed in this paper. As a switched linear system considered consists of several discrete-time linear time-invariant(LTI) systems, a sufficient and necessary condition for state non-overshooting of discrete-time LTI systems is derived firstly, and the non-overshooting region, which is a pair of 0-symmetrical cones, is defined and discussed. Then, using the idea of dividing the state space into distinct non-overshooting regions–a subsystem corresponding to a one, some conditions for state non-overshooting of discrete-time switched linear systems are inferred by using the well-known S-procedure. Finally, some output non-overshooting conditions were set up in a similar way.

The presented paper considers an unconstrained local controllability problem of semilinear fractional order discrete-time systems with constant delay in control. By the general formula of solution of difference state equation we present a sufficient condition for local unconstrained controllability. At the end, an illustrative example is presented.

This paper propose a novel design procedure for output-feedback switching linear parameter-varying (LPV) controllerS. The switching controller which include several LPV controllers designed beforehand and independently with corresponding $\text{H}_{\infty}$ control performance criteria. The new procedure based on the Youla parameterization ideas, state space realization of free parameters of these LPV controllers is achieved. This realization ensures that each switching point satisfy the $\text{H}_{\infty}$ performance under arbitrary switching. The effectiveness of the proposed method is demonstrated with a numerical example.

In this paper, we consider the finite horizon $H_{2}/H_{\infty}$ control problem for linear stochastic differential equations (SDEs) with infinite Markovian jumps. A necessary and sufficient condition is proposed for the existence of the mixed $H_{2}/H_{\infty}$ control by means of the solvability of the coupled difference Riccati equations (CDREs). Moreover, the state feedback $H_{2}/H_{\infty}$ controller is constructed through the solution of CDREs.

This paper discusses $l_{p}$ induced norms and a small-gain theorem for discrete-time stochastic systems. The induced norm of systems generally depends on the associated input space of the systems. At the beginning, we consider a general stochastic $l_{p}$ space and introduce the primitive $l_{p}$ induced norm based on the space. However, the primitive $l_{p}$ induced norm can actually be confirmed not to reflect the nature of the randomness behind the stochastic systems, which leads us to overestimating its value. Hence, we take a proper subspace of the stochastic $l_{p}$ space and introduce another $l_{p}$ induced norm based on the subspace. We demonstrate with examples that the norm based on the subspace successfully reflects the nature of the system randomness. Then, we give the small-gain theorem based on the norm.

This paper introduces the concept of normalized bicoprime factorizations. The notion of a normalized bicoprime factorization is first defined and conditions for normalization are given in state space. Algorithms that can be used to obtain a normalized bicoprime factorization of the plant are presented.

The problem of estimating the reachable sets of an impulsive control system with uncertainty in the initial data is considered. The initial states are not known exactly, but belong to a given star-shaped symmetric nondegenerate polytope. Impulsive controls in a dynamical system are vectors and belong to the generalized ellipsoid in the space of functions of bounded variation. Algorithms for constructing ellipsoidal estimates of reachable sets for such control systems are presented in the paper.

This paper is concerned with the admissibility analysis for a kind of stochastic singular delayed systems (SSDSs). Sufficient conditions for the regularity of the impulse-free solution to the SSDSs are obtained. Consequently, by formulating Lyapunov-Krasovskii functional and applying Ito formula, novel sufficient conditions for the stability of SSDSs are derived in terms of strict linear matrix inequalities (LMIs). An illustrative example is used to demonstrate the effectiveness and usefulness of the obtained results.

In this paper, robust stability and perturbations rejection of perturbed nonlinear systems with disturbance are considered by using the operator-based right coprime factorization technique. That is, when both perturbation and disturbance exist in nonlinear systems, robust control design scheme is proposed for guaranteeing the uncertain nonlinear systems to work stable based on the proposed condition using bilinear operators. Meanwhile, based on the proposed bilinear operator, the perturbations rejection is discussed by combining the proposed operator controller. The proposed design scheme not only guarantees robust stability for the uncertain nonlinear system, but also realizes removing the adverse effects resulting from the perturbations such that tracking performance is achieved. Finally, a simulation example is given to confirm the effectiveness of the proposed design scheme.

This paper focuses on the task of safety controller synthesis, that is, designing a controller that will take a system from any point within a compact set of initial states to a point inside a set of acceptable goal states, while never entering any state that is deemed unsafe. To do this we use a human generated trajectory-based approach. We introduce the control autobisimulation function, which is the analog of the control Lyapunov function for approximate bisimulation. We consider a class of hybrid systems and use this function to determine a set of admissible feedback control laws that guarantee trajectory robustness for underlying dynamics that are linear affine, feedback linearizable, and differentially flat. This property ensures that any trajectory of the closed-loop system that is initialized within some neighborhood of a nominal trajectory will stay within some tube of the nominal trajectory when given the same input. This feedback control and input can be used as the controller for some subset of the initial states. We demonstrate how to combine multiple trajectories into a synthesized controller that satisfies the safety problem.

The computational costs of the parameter space approach, which is used to calculate the stability boundaries for linear time-invariant systems (LTI), increase fast with the dimension of the investigated system. In this paper, the authors present a successive approximation of the stability boundaries for large scale systems. The approximation provides a fast and accurate estimation of the stability boundaries. Furthermore, the approximation converges to the stability boundaries of the large scale system and points, that are not stable, are never classified as stable during approximation. Thus, the new method enables the applicability of the parameter space approach to large scale systems by greatly reducing the computational costs.

This paper is concerned with the controller design for a one dimensional Schrodinger equation with an input delay on the boundary. A state-feedback control law is presented via the backstepping method to stabilize the delayed system. The numerical simulation verifies the feasibility of the suggested control law.

The paper presents an algorithm for constructing of synthesizing control function. This algorithm is sufficiently convenient for numerical implementation and a wide class of nonlinear systems of ordinary differential equations, provide the passage from initial state into an arbitrary given state. We obtain a constructive condition for the choice of finish state for which the passage is possible with regard of the constraints imposed on the control.

This paper is devoted to discuss the implications of the Kalman-Yakubovich-Popov Lemma, so-called also Positive Real Lemma, when non-minimal state space realizations of transfer matrices of linear continuous systems are used. It is seen that some extra parametrical conditions for positive realness of the transfer matrix to be equivalent to the stability Lemma from a Lyapunov equation with extended constraints appear on the non-minimal parameterizations. Those extra conditions are, in fact, spurious since stable cancellations do not affect to the nature (positive real or not) of the associate transfer matrix.

Consider a formation control problem in which agents in Euclidean space are tasked with stabilizing their positions at prescribed target distances from each other, and for which these distances are described by a rigid graph. There is a mismatch in target distances if there is a pair of neighboring agents i and j such that agent i aims to stabilize from agent j at a distance d ij , but agent j from agent i at a slightly different distance d′ ij . A mismatch in target distances results in a mismatch in the associated interaction laws. It was shown in a recent paper [1] that when there is a small mismatch in the interaction laws, the entire formation undergoes a constant rigid motion. In this work, we build on this observation to establish a controllability result. Specifically, given that there is a selected subset of agents that can control the mismatches in interactions among them, we show that if these agents are fully connected and form a nondegenerate triangle (or more generally, a nondegenerate k-simplex in the k-dimensional case), then it is possible to control an arbitrary rigid motion of the entire formation.

This paper is concerned with the Hankel operator and the Hankel norm of sampled-data systems. Even though these systems are intrinsically periodically time-varying, no studies have taken this important feature into account in the treatment of the Hankel operator / norm. We characterize the Hankel operator / norm of sampled-data systems adequately under the treatment with the L 2 -type norm for the past input and the L ∞ -type norm for the future output. Such treatment still captures the essential issue on the periodicity but contributes to neat arguments compared with the case when the L 2 -type norm were also considered on the future output.

This paper investigates the robust control of a class of minimally infinitesimally rigid formations in the face of constant bias in the measurements of relative positions between neighboring agents. It is shown that by appropriately modifying standard gradient controls, desired formation shape can be achieved up to small errors in relative positions.

This paper discusses the global controllability for a class of 3-dimensional nonlinear systems with two inputs. Firstly, we retrospect the difficulty and progress for the study of the global controllability of higher dimensional nonlinear systems. Secondly, we present a necessary and sufficient condition for the global controllability of 3-dimensional nonlinear system with two inputs under some assumptions. All conditions are imposed on the structure of the system only. Finally, we give some examples to show the application of our results.

In this paper, stabilizability subspaces for linear impulsive systems are defined by the property that not only can trajectories be maintained within the subspace by suitable control signals, they can also be made to asymptotically converge to the equilibrium at the origin. Previous work on state feedback stabilization and the study of controlled invariant subspaces for linear impulsive systems is combined to yield a state feedback characterization of stabilizability subspaces.

This paper presents a balanced truncation technique for model and scheduling order-reduction (i.e. reduction of number of states as well as of scheduling parameters) of exponentially stable temporal- and spatial-LPV interconnected systems. The reduction is based on the application of the full block S-procedure, using both Constant Gramians (CGs) and Parameter-Dependent Gramians (PDGs). The reduced models preserve exponential stability and the spatial structure of the system. The proposed method is demonstrated on an experimentally identified spatially interconnected model of an actuated beam.

In this paper we derive necessary and sufficient Person by Person and Global (team) decentralized optimality conditions, for stochastic differential decision problems with multiple Decision Makers (DMs) or Agents aimed at optimizing a common pay-off. These consist of forward and backward stochastic differential equations, and a set of conditional variational Hamiltonians with respect to the information structures of the DMs. © 2016 IEEE. 6161 6166

This paper addresses the infinite-horizon optimal control problem for max-plus linear systems where the considered objective function is a sum of discounted stage costs over an infinite horizon. The minimization problem of the cost function is equivalently transformed into a maximization problem of a reward function. The resulting optimal control problem is solved based on an optimistic planning algorithm. The control variables are the increments of system inputs and the action space is discretized as a finite set. Given a finite computational budget, a control sequence is returned by the optimistic planning algorithm. The first control action or a subsequence of the returned control sequence is applied to the system and then a receding-horizon scheme is adopted. The proposed optimistic planning approach allows us to limit the computational budget and also yields a characterization of the level of near-optimality of the resulting solution. The effectiveness of the approach is illustrated with a numerical example. The results show that the optimistic planning approach results in a lower tracking error compared with a finite-horizon approach when a subsequence of the returned control sequence is applied.

This paper addresses the optimality of stochastic control strategies based on the infinite horizon average cost criterion, subject to total variation distance ambiguity on the conditional distribution of the controlled process. This stochastic optimal control problem is formulated using minimax theory, in which the minimization is over the control strategies and the maximization is over the conditional distributions. Under the assumption that, for every stationary Markov control law the maximizing conditional distribution of the controlled process is irreducible, we derive a new dynamic programming recursion which minimizes the future ambiguity, and we propose a new policy iteration algorithm. The new dynamic programming recursion includes, in addition to the standard terms, the oscillator semi-norm of the cost-to-go. The maximizing conditional distribution is found via a water-filling algorithm. The implications of our results are demonstrated through an example. © 2015 IEEE. 54rd IEEE Conference on Decision and Control,CDC 2015 7171 7176

To find the optimal nonlinear separating boundary with maximum margin in the input data space, this paper proposes Contractive Rectifier Networks (CRNs), wherein the hidden-layer transformations are restricted to be contraction mappings. The contractive constraints ensure that the achieved separating margin in the input space is larger than or equal to the separating margin in the output layer. The training of the proposed CRNs is formulated as a linear support vector machine (SVM) in the output layer, combined with two or more contractive hidden layers. Effective algorithms have been proposed to address the optimization challenges arising from contraction constraints. Experimental results on MNIST, CIFAR-10, CIFAR-100 and MIT-67 datasets demonstrate that the proposed contractive rectifier networks consistently outperform their conventional unconstrained rectifier network counterparts.

In this paper, the optimal H2 control problem for spatially invariant systems is considered. The framework adopted is borrowed from the work pioneered by Voulgaris et al. In particular, the H2 optimal control problem is solved via the computation of an orthogonal projection of a tensor Hilbert space onto a particular subspace. Next, the optimal H2 decentralized control problem is solved by computing an orthogonal projection on a class of Youla parameters with a decentralized structure. The latter uses Riesz projections after invoking a particular L2-basis.

In this paper we prove that approximate and exact controllability are equivalent properties for general closed finite-dimensional quantum systems.

This paper investigates some controllability properties of probabilistic discrete dynamic systems. Related approximate probabilistic controllability properties are also dealt with for the case when a nominal controllable system is subject to either parametrical perturbations or unmodeled dynamics.

In distributed systems, a common question is how to synthesize a control law that adheres to the system's distributed interconnection structure. One promising synthesis approach involves encoding the system's interconnections as a pattern in the system matrices, and carrying this pattern through all steps of a control design. To date, though, all control results on this front have had limitations on which distributed structures are admissible. In this paper, we provide a pole placement result that is valid for more general system patterns. We also show that a system's controllability does not imply patterned pole placement, so we introduce a novel notion of controllability for patterned distributed systems.

In this paper, we focus on Cuckoo Search (CS) that is one of metaheuristics, and propose an adaptive CS to improve its search performance and usability. First, we analyze basically and qualitatively the effects of CS's parameter on its search dynamics. Second, from the analysis results, we define an indicator that evaluates the search state of CS based on the effective metaheuristics strategy. Moreover, based on the indicator, we construct a new mechanism to control the search state by adaptively adjusting a parameter of CS. The performance of the proposed adaptive CS with the parameter adjustment mechanism is verified through numerical simulations for several types of typical benchmark problems.

In the paper a differential system is considered, which state is described by a parabolic initial boundary value problem with distributed parameters on a graph. Control action and observations occur simultaneously. The existence conditions of a unique control action and the controllability system are obtained.

This paper deals with the complete controllability of impulsive semilinear stochastic retarded system under the assumption that the corresponding linear system is completely controllable Sufficient conditions for the proposed problem in finite dimensional are established by using Banach fixed point theorem. Finally, one example is provided to illustrate the application of the obtained results.

In the paper, a fractional linear continuous control system with the Hilfer derivative is considered. An existence and uniqueness of a solution to such system is investigated. Based on the existence result, a theorem on the continuous dependence of solutions on controls to such problem is proved.

In this paper we present a right inversion scheme based on the essential concept of reachability. This scheme inverts a Hurwitz stable system one step ahead. We illustrate our procedure with the simulation of an ideal inverted pendulum.

In order to design efficient algorithms that work on the set of controllers that fulfill a given property, e.g., stability or a norm bound, it is important to have an operation that preserves that property, i.e., a suitable blending method. While available approaches use the Youla parameters in order to define this operation for stability in a trivial way, they do not provide a general answer to the problem. This paper places the controller blending problem in a more general setting by pointing to the basic global geometric structures that are related to feedback stability or suboptimal ℋ ∞ design. A detailed analysis is given for feedback stability: an operation is given under which well-posedness is a group while stability is a semigroup. Moreover, an operation is given that makes controllers with strongly stable property a group.

In this paper we use martingale techniques to derive a sufficient condition for existence of decentralized strategies in non-cooperative stochastic differential games. The sufficient condition is given by decentralized conditional Isaacs conditions, linked to backward stochastic differential equations, whose solutions are related to the value processes of each one of the Decision Makers (DMs) or Players of the game. Our formulation and results include decentralized noncooperative stochastic games with mean field and conditional mean field components. © 2015 IEEE. 54rd IEEE Conference on Decision and Control,CDC 2015 7832 7837

In this paper, geometric nonlinearity of a flexible link is considered for dynamic modeling of free-floating space manipulators. The system dynamics is derived by Lagrange theorem in conjunction with the assumed modes method. By reducing some parameters, dynamic equations of small deflection is obtained for control system design. For position control design, modified partial feedback linearization control is developed with the parameter optimization process by genetic algorithm. Position control performances based on models without considering geometric nonlinearity are illustrated by numerical simulations. The simulation results demonstrate that even in the condition of large deflections, the position control law based on models considering small deflections can also reach a good performance of IAE (Integral of the Absolute value of Error).