Stochastic Control Analysis Research Articles

Optimal lock-down intensity: A stochastic pandemic control approach of path integral

Abstract The aim of this article is to determine the optimal intensity of lock-down measures and vaccination rates to control the spread of coronavirus disease 2019. The study uses a stochastic susceptible-infected-recovered (SIR) model with infection dynamics. A Feynman-type path integral control approach is used to derive a forward Fokker-Plank-type equation for the system, which helps in performing a stochastic control analysis. The simulation study concludes that increasing the diffusion coefficients leads to a downward trend in the susceptible and recovery curves, while the infection curve becomes ergodic. Additionally, the study shows that the optimal lock-down intensity is stable around zero, and the vaccination rate increases over time.

Chance-constrained [formula omitted] control for a class of time-varying systems with stochastic nonlinearities: The finite-horizon case

In this paper, a new finite-horizon H∞ control problem is considered for a class of time-varying systems with stochastic nonlinearities, measurements degradation and chance constraints. The purpose of the addressed problem is to design the time-varying controller such that the closed-loop system satisfies the prespecified H∞ disturbance attenuation requirement and certain chance constraints on the controlled output vector zk (i.e., the probability of the controlled output zk belonging to a given set is larger than a prescribed value). A modified maximum-volume-inscribed-ellipsoid (MVIE) method is employed to convert the chance constraint into some tractable inequalities, which could be conveniently handled by the recursive linear matrix inequality (RLMI) approach. Then, by using stochastic control analysis method, sufficient conditions are derived for the existence of the desired multi-objective controller and, furthermore, the gains of the desired controllers are characterized by means of RLMIs. Finally, two illustrative examples and a practical system are proposed to highlight the effectiveness and applicability of the presented controller design technology.

Controlling E. coli Gene Expression Noise.

Intracellular protein copy numbers show significant cell-to-cell variability within an isogenic population due to the random nature of biological reactions. Here we show how the variability in copy number can be controlled by perturbing gene expression. Depending on the genetic network and host, different perturbations can be applied to control variability. To understand more fully how noise propagates and behaves in biochemical networks we developed stochastic control analysis (SCA) which is a sensitivity-based analysis framework for the study of noise control. Here we apply SCA to synthetic gene expression systems encoded on plasmids that are transformed into Escherichia coli. We show that (1) dual control of transcription and translation efficiencies provides the most efficient way of noise-versus-mean control. (2) The expressed proteins follow the gamma distribution function as found in chromosomal proteins. (3) One of the major sources of noise, leading to the cell-to-cell variability in protein copy numbers, is related to bursty translation. (4) By taking into account stochastic fluctuations in autofluorescence, the correct scaling relationship between the noise and mean levels of the protein copy numbers was recovered for the case of weak fluorescence signals.

Uplink Power Adjustment in Wireless Communication Systems: A Stochastic Control Analysis

This paper considers mobile to base station power control for lognormal fading channels in wireless communication systems within a centralized information stochastic optimal control framework. Under a bounded power rate of change constraint, the stochastic control problem and its associated Hamilton-Jacobi-Bellman (HJB) equation are analyzed by the viscosity solution method; then the degenerate HJB equation is perturbed to admit a classical solution and a suboptimal control law is designed based on the perturbed HJB equation. When a quadratic type cost is used without a bound constraint on the control, the value function is a classical solution to the degenerate HJB equation and the feedback control is affine in the system power. In addition, in this case we develop approximate, but highly scalable, solutions to the HJB equation in terms of a local polynomial expansion of the exact solution. When the channel parameters are not known a priori, one can obtain on-line estimates of the parameters and get adaptive versions of the control laws. In numerical experiments with both of the above cost functions, the following phenomenon is observed: whenever the users have different initial conditions, there is an initial convergence of the power levels to a common level and then subsequent approximately equal behavior which converges toward a stochastically varying optimum.