Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
Finiteness results for sigmoidal “neural” networks
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Polynomial bounds for VC dimension of sigmoidal neural networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Polynomial bounds for VC dimension of sigmoidal and general Pfaffian neural networks
Journal of Computer and System Sciences - Special issue: dedicated to the memory of Paris Kanellakis
Probabilistic robustness analysis: explicit bounds for the minimum number of samples
Systems & Control Letters
NP-Hardness of Some Linear Control Design Problems
SIAM Journal on Control and Optimization
Brief Some applications of randomized algorithms for control system design
Automatica (Journal of IFAC)
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
Brief Probabilistic solutions to some NP-hard matrix problems
Automatica (Journal of IFAC)
Some Problems of Robust Control of a Stochastic Object
Automation and Remote Control
A survey of randomized algorithms for control synthesis and performance verification
Journal of Complexity
Polytopic best-mean H∞performance analysis
AEE'08 Proceedings of the 7th WSEAS International Conference on Application of Electrical Engineering
Robustness of Isotropic Stable Mutations in a General Search Space
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
Randomized model predictive control for robot navigation
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
A probabilistic particle-control approximation of chance-constrained stochastic predictive control
IEEE Transactions on Robotics
Evolutionary algorithms with stable mutations based on a discrete spectral measure
ICAISC'10 Proceedings of the 10th international conference on Artifical intelligence and soft computing: Part II
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
Brief Some applications of randomized algorithms for control system design
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
A probabilistic framework for problems with real structured uncertainty in systems and control
Automatica (Journal of IFAC)
Probabilistic design of LPV control systems
Automatica (Journal of IFAC)
Convexity and convex approximations of discrete-time stochastic control problems with constraints
Automatica (Journal of IFAC)
Hi-index | 22.16 |
By now it is known that several problems in the robustness analysis and synthesis of control systems are NP-complete or NP-hard. These negative results force us to modify our notion of ''solving'' a given problem. An approach that is recently gaining popularity is that of using randomized algorithms, which can be used to solve a problem approximately, most of the time. We begin with the premise that many problems in robustness analysis and synthesis can be formulated as the minimization of an objective function with respect to the controller parameters. It is argued that, in order to assess the performance of a controller as the plant varies over a prespecified family, it is better to use the average performance of the controller as the objective function to be minimized, rather than its worst-case performance, as the worst-case objective function usually leads to rather conservative designs. Then it is shown that a property from statistical learning theory known as uniform convergence of empirical means (UCEM) plays an important role in allowing us to construct efficient randomized algorithms for a wide variety of controller synthesis problems. In particular, whenever the UCEM property holds, there exists an efficient (i.e., polynomial-time) randomized algorithm. Using very recent results in statistical learning theory, it is shown that the UCEM property holds in any problem in which the satisfaction of a performance constraint can be expressed in terms of a finite number of polynomial inequalities. In particular, several problems such as robust stabilization and weighted H"2/H"~-norm minimization are amenable to the randomized approach.