Risk-Constrained Control of Mean-Field Linear Quadratic Systems

The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low-probability yet statistically significant (risky) events. The present research focuses on infinite-horizon risk-constrained linear quadratic regulators in a mean-field setting. We address the risk constraint by bounding the cumulative one-stage variance of the state penalty of all players. It is shown that the optimal controller is affine in the state of each player with an additive term that controls the risk constraint. In addition, we propose a solution independent of the number of players. Finally, simulations are presented to verify the theoretical findings.Comment: Accepted at 62nd IEEE Conference on Decision and Contro

Determination of Thermal Barrier Coatings Layers Optimum Thickness via PSO-SA Hybrid Optimization Method concerning Thermal Stress

Turbine entry temperature of turbo-engines has been increased to improve proficiency. Consequently, protecting the hot section elements experiencing aggressive service conditions necessitates the applying of thermal barrier coatings (TBC). Developing TBC systems and improving performance is an ongoing endeavour to prolong the lifetime. Thus, various studies have been conducted to find the optimum properties and dimensions. In this paper, the optimum thickness of intermediate bond coat (BC) and top coat (TC) have been determined via a novel hybrid particle swarm and simulated annealing stochastic optimization method. The optimum thicknesses have been achieved under the constraint of thermal stress induced by thermal fatigue, creep, and oxidation in the TC while minimizing the weight during twenty cycles. The solutions for BC and TC thicknesses are respectively 50 μm and 450 μm. Plane stress condition has been adopted for theoretical and finite element stress analysis, and the results are successfully compared

Optimization in Dynamical Systems: Theory and Application

In this dissertation, we study optimization methods in interconnected systems and investigate their applications in robotics, energy harvesting, and mean-field linear quadratic multi-agent systems. We first focus on parallel robots. Parallel Robots have numerous applications in motion simulation systems and high-precision instruments. Specifically, we investigate the forward kinematics (FK) of parallel robots and formulate it as an error minimization problem. Following this formulation, we develop an optimization algorithm to solve FK and provide a theoretical analysis of the convergence of the proposed algorithm. Then, we investigate the energy optimization (maximization) in a specific class of micro-energy harvesters (MEH). These types of energy harvesters are known to extract the largest amount of power from the kinetic energy of the human body, making them an appropriate choice for wearable technology in healthcare applications. Employing machine learning tools and using the existing models for the MEH's kinematics, we propose three methods for energy maximization. Next, we study optimal control in a mean-field linear quadratic system. Mean-field systems have critical applications in approximating very large-scale systems' behavior. Specifically, we establish results on the convergence of policy gradient (PG) methods to the optimal solution in a mean-field linear quadratic game. We finally consider the risk-constrained control of agents in a mean-field linear quadratic setting. Simulations validate the theoretical findings and their effectiveness

Reinforcement Learning in Deep Structured Teams: Initial Results with Finite and Infinite Valued Features

In this paper, we consider Markov chain and linear quadratic models for deep structured teams with discounted and time-average cost functions under two non-classical information structures, namely, deep state sharing and no sharing. In deep structured teams, agents are coupled in dynamics and cost functions through deep state, where deep state refers to a set of orthogonal linear regressions of the states. In this article, we consider a homogeneous linear regression for Markov chain models (i.e., empirical distribution of states) and a few orthonormal linear regressions for linear quadratic models (i.e., weighted average of states). Some planning algorithms are developed for the case when the model is known, and some reinforcement learning algorithms are proposed for the case when the model is not known completely. The convergence of two model-free (reinforcement learning) algorithms, one for Markov chain models and one for linear quadratic models, is established. The results are then applied to a smart grid.Comment: This version corrects some typographical error

Evaluation of the efficacy of Mannitol and overhydration in anesthesia for kideny grafting

History and Objectives: Considering the incidence and incremental trend for kidney grafting and the significance of initiation of diuresis and the positive effect of mannitol and overhydration and for evaluation of simultaneous use of them, this study was carried out on referrals of Labafinejad hospital in 2000. Materials and Methods: The quasi-experimental strategy of this study was carried out on 40 patients with indications for kidney grafting with their written consent. Twenty min before anastomosis of renal vein, intravenous injection of mannitol (5 ml/kg) was initiated and its effect on the initiation of diuresis in min was recorded with a confidence interval of 95. Results: This study was performed on 40 patients (25 females and 15 males) with an average age of 33.6 years and average weight of 52.6kg. The results showed that in 80 of patients, diuresis was initiated in less than a minute and in 90 of them, diuresis was initiated in less than 2 min. Conclusion and Recommendations: Simultaneous use of mannitol and overhydration could accelerate the initiation of diuresis and because this is very important in survival of grafted kidney, therefore it recommended to carry out thorough experimental study

On Forward Kinematics of a 3SPR Parallel Manipulator

In this paper, a new numerical method to solve the forward kinematics (FK) of a parallel manipulator with three-limb spherical-prismatic-revolute (3SPR) structure is presented. Unlike the existing numerical approaches that rely on computation of the manipulator's Jacobian matrix and its inverse at each iteration, the proposed algorithm requires much less computations to estimate the FK parameters. A cost function is introduced that measures the difference of the estimates from the actual FK values. At each iteration, the problem is decomposed into two steps. First, the estimates of the platform orientation from the heave estimates are obtained. Then, heave estimates are updated by moving in the gradient direction of the proposed cost function. To validate the performance of the proposed algorithm, it is compared against a Jacobian-based (JB) approach for a 3SPR parallel manipulator