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- articleMarch 2006
Zero-Sum Ergodic Stochastic Games with Feller Transition Probabilities
SIAM Journal on Control and Optimization (SICON), Volume 45, Issue 3Pages 773–789https://doi.org/10.1137/S0363012904443257We consider zero-sum stochastic games with Borel state spaces satisfying a generalized geometric ergodicity condition. The main objective of this paper is to establish a minimax theorem for a class of ergodic stochastic games with the Feller transition ...
- articleAugust 2005
A Bounded Variation Control Problem for Diffusion Processes
SIAM Journal on Control and Optimization (SICON), Volume 44, Issue 2Pages 389–417https://doi.org/10.1137/S0363012903436119We consider an infinite horizon discounted cost minimization problem for a one-dimensional stochastic differential equation model. The available control is an added bounded variation process. The cost structure involves a running cost function and a ...
- articleSeptember 2000
Average Cost Dynamic Programming Equations For Controlled Markov Chains With Partial Observations
SIAM Journal on Control and Optimization (SICON), Volume 39, Issue 3Pages 673–681https://doi.org/10.1137/S0363012998345172The value function for the average cost control of a class of partially observed Markov chains is derived as the "vanishing discount limit," in a suitable sense, of the value functions for the corresponding discounted cost problems. The limiting ...
- articleAugust 1999
Stability of Piecewise-Deterministic Markov Processes
SIAM Journal on Control and Optimization (SICON), Volume 37, Issue 5Pages 1483–1502https://doi.org/10.1137/S0363012997330890In this paper, we study a form of stability for a general family of nondiffusion Markov processes known in the literature as piecewise-deterministic Markov process (PDMP). By stability here we mean the existence of an invariant probability measure for ...
- articleAugust 1999
Averaging Method for One-Sided Lipschitz Differential Inclusions with Generalized Solutions
SIAM Journal on Control and Optimization (SICON), Volume 37, Issue 5Pages 1600–1613https://doi.org/10.1137/S0363012997321371We investigate the convergence of the solution set for singularly perturbed differential inclusions using an averaging technique. The limits of the fast solutions are considered as generalized solutions (i.e., Radon probability measures) of the ...
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- articleApril 1999
Relaxation of Control Systems Under State Constraints
SIAM Journal on Control and Optimization (SICON), Volume 37, Issue 4Pages 1291–1309https://doi.org/10.1137/S0363012997331019In this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control. In particular, we show that the Mangasarian--Fromowitz constraint qualification allows us to rewrite ...
- articleMarch 1998
Discretized Maximum Likelihood and Almost Optimal Adaptive Control of Ergodic Markov Models
SIAM Journal on Control and Optimization (SICON), Volume 36, Issue 2Pages 422–446https://doi.org/10.1137/S0363012996298369Three distinct controlled ergodic Markov models are considered here. The models are a discrete time controlled Markov process with complete observations, a controlled diffusion process with complete observations, and a discrete time controlled Markov ...
- articleMarch 1998
Existence of Markov Controls and Characterization of Optimal Markov Controls
SIAM Journal on Control and Optimization (SICON), Volume 36, Issue 2Pages 609–653https://doi.org/10.1137/S0363012995295516Given a solution of a controlled martingale problem it is shown under general conditions that there exists a solution having Markov controls which has the same cost as the original solution. This result is then used to show that the original stochastic ...
- articleJanuary 1998
Infinite Linear Programming and Multichain Markov Control Processes in Uncountable Spaces
SIAM Journal on Control and Optimization (SICON), Volume 36, Issue 1Pages 313–335https://doi.org/10.1137/S0363012995292238In this paper we use infinite linear programming to study Markov control processes in Borel spaces and the average cost criterion in the "unichain" and "multichain" cases. Under appropriate assumptions we show that in both cases the associated linear ...
- articleSeptember 1997
Tracking Fast Trajectories Along a Slow Dynamics: A Singular Perturbations Approach
Controlled coupled slow and fast motions are examined in a singular perturbations setting. The objective is to minimize a cost functional that takes into account both the fast motion, supposing, say, tracking a fast target, and the slow dynamics. A ...
- articleSeptember 1997
Risk-Sensitive Control of Finite State Machines on an Infinite Horizon I
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 5Pages 1790–1810https://doi.org/10.1137/S0363012995291622In this paper we consider robust and risk-sensitive control of discrete time finite state systems on an infinite horizon. The solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game. ...
- articleSeptember 1997
Nonlinear Uncertain Systems and Necessary Conditions of Optimality
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 5Pages 1755–1772https://doi.org/10.1137/S0363012995285569In this paper we consider an optimal control problem for a class of systems governed by nonlinear evolution equations containing a nonlinear monotone operator and a nonmonotone operator with uncertain parameters. We prove existence of solutions and ...
- articleSeptember 1997
Weighted Means in Stochastic Approximation of Minima
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 5Pages 1811–1827https://doi.org/10.1137/S0363012995283789Weighted averages of Kiefer--Wolfowitz-type procedures, which are driven by larger step lengths than usual, can achieve the optimal rate of convergence. A priori knowledge of a lower bound on the smallest eigenvalue of the Hessian matrix is avoided. The ...
- articleJuly 1997
Min-Max Characterization of a Small Noise Limit on Risk-Sensitive Control
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 4Pages 1093–1115https://doi.org/10.1137/S0363012995279420Stochastic control problems on a finite horizon with exponential cost criteria are considered. By taking a kind of singular limit a Hamilton--Jacobi--Isaacs equation is obtained. Its solution is characterized as the lower value function of a ...
- articleJuly 1997
Regularity Properties of the Phase for Multivariable Systems
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 4Pages 1366–1386https://doi.org/10.1137/S0363012994279243For multivariable, input-output systems that are represented as rational, transfer-function matrices, the most frequently used measures of relative stability are gain based. However, there are a number of important physical applications where the phase ...
- articleJuly 1997
${\cal H}_\infty$ Control and Estimation Problems with Delayed Measurements: State-Space Solutions
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 4Pages 1217–1243https://doi.org/10.1137/S0363012994277499Most physical processes exhibit transport delay in the measured output, and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for. In this paper, we give necessary and sufficient conditions ...
- articleJuly 1997
Finite-Dimensional Filters with Nonlinear Drift VII: Mitter Conjecture and Structure of $\eta$
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 4Pages 1116–1131https://doi.org/10.1137/S0363012994272836The concept of estimation algebra introduced independently by Brockett and Mitter has been playing a fundamental role in the investigation of finite-dimensional nonlinear filters. Mitter conjectured that the observation terms $h_i(x)$ are polynomials of ...
- articleJuly 1997
A General Stochastic Outer Approximations Method
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 4Pages 1387–1421https://doi.org/10.1137/S0363012994263202Optimization problems involving an infinite number of constraints are considered. This paper presents a general stochastic outer approximations method which incorporates mechanisms for active search of relevant constraints and for dropping of irrelevant ...
- articleMay 1997
Optimization of Observations: a Stochastic Control Approach
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 3Pages 1030–1052https://doi.org/10.1137/S0363012995287878We study a stochastic control problem for the optimization of observations in a partially observable stochastic system. Using a method of discontinuous time transformation, we associate with the original problem with unbounded controls a problem that ...
- articleMay 1997
On the Puiseux Series Expansion of the Limit Discount Equation of Stochastic Games
SIAM Journal on Control and Optimization (SICON), Volume 35, Issue 3Pages 860–875https://doi.org/10.1137/S0363012995284138In this paper we give a new proof of the existence of Puiseux series expansion of the limit discount equation of finite state stochastic games. Unlike the original proof, due to Bewley and Kohlberg [ Math. Oper. Res., 3 (1976), pp. 197--208], our proof ...