1,721,007 research outputs found
On mean square boundedness of stochastic linear systems with bounded controls
No full textWe start by summarizing the state of the art in stabilization of stochastic linear systems with bounded inputs and highlight remaining open problems. We then report two new results concerning mean-square boundedness of a linear system with additive stochastic noise. The first states that, given any nonzero bound on the controls, it is possible to construct a policy with bounded memory requirements that renders a marginally stable stabilizable system mean-square bounded in closed-loop. The second states that it is not possible to ensure mean-square boundedness in closed-loop with a bounded control policy for systems affected by unbounded noise and having at least one eigenvalue outside the unit circle
On mean-square boundedness of stochastic linear systems with quantized observations
No full textWe propose a procedure to design a state-quantizer with a fixed finite alphabet for a Lyapunov stable stochastic linear system, and a bounded policy based on the resulting quantized state measurements to ensure bounded second moments of the states in closed-loop
Stable Networked Control Systems With Bounded Control Authority
No full textWe study the stability of a class of networked control systems with hard bounds on the control authority. The plant dynamics are discrete-time, linear, and time-invariant, with stochastic process noise and measurement noise. The controller is designed as a norm-bounded causal history-dependent function of the past outputs perturbed by bounded noise. The resulting control signals are assumed to be transmitted through a lossy channel with packet dropouts. We show that under mild assumptions on the system matrices, the statistics of the process and measurement noise sequences, and the probability of dropouts, it is possible to ensure bounded variance of the system in closed-loop
Isospectral flows on a class of finite-dimensional Jacobi matrices
No full textWe present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes n×n zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e. features a right-hand side with a nested commutator of matrices and structurally resembles the double-bracket o.d.e. studied by R.W. Brockett in 1991. We prove that its solutions converge asymptotically, that the limit is block-diagonal, and above all, that the limit matrix is defined uniquely as follows: for n even, a block-diagonal matrix containing 2×2 blocks, such that the super-diagonal entries are sorted by strictly increasing absolute value. Furthermore, the off-diagonal entries in these 2×2 blocks have the same sign as the respective entries in the matrix employed as the initial condition. For n odd, there is one additional 1×1 block containing a zero that is the top left entry of the limit matrix. The results presented here extend some early work of Kac and van Moerbeke
Stable stochastic receding horizon control of linear systems with bounded control inputs
No full textStochastic receding horizon control with output feedback and bounded controls
No full textWe study the problem of receding horizon control for stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. We prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions. We also discuss how some quantities required by the finite-horizon optimization problem can be computed off-line, thus reducing the on-line computation
Stochastic receding horizon control with output feedback and bounded control inputs
No full textWe study the problem of receding horizon control of stochastic discrete-time systems with bounded control inputs and incomplete state information. Given a suitable choice of causal control policies, we first present a slight extension of the Kalman filter to estimate the state optimally in mean-square sense. We then show how to augment the underlying optimization problem with a negative drift-like constraint, yielding a second-order cone program to be solved periodically online. Finally, we prove that the receding horizon implementation of the resulting control policies renders the state of the overall system mean-square bounded under mild assumptions
On the connections between PCTL and dynamic programming
No full textProbabilistic Computation Tree Logic (PCTL) is a well-known modal logic which has become a standard for expressing temporal properties of finite-state Markov chains in the context of automated model checking. In this paper, we consider PCTL for noncountable-space Markov chains, and we show that there is a substantial affinity between certain of its operators and problems of Dynamic Programming. We prove some basic properties of the solutions to the latter. We also provide two examples and demonstrate how recovery strategies in practical applications, which are naturally stated as reach-avoid problems, can be viewed as particular cases of PCTL formulas
Attaining mean square boundedness of a marginally stable noisy linear system with a bounded control input
No full textWe construct control policies that ensure bounded variance of a noisy marginally stable linear system in closed-loop. It is assumed that the noise sequence is a mutually independent sequence of random vectors, enters the dynamics affinely, and has bounded fourth moment. The magnitude of the control is required to be of the order of the first moment of the noise, and the policies we obtain are simple and computable
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