Stabilization of the Cart–Inverted-Pendulum System Using State-Feedback Pole-Independent MPC Controllers

In this paper, a pole-independent, single-input, multi-output explicit linear MPC controller is proposed to stabilize the fourth-order cart–inverted-pendulum system around the desired equilibrium points. To circumvent an obvious stability problem, a generalized prediction model is proposed that yields an MPC controller with four tuning parameters. The first two parameters, namely the horizon time and the relative cart–pendulum weight factor, are automatically adjusted to ensure a priori prescribed system gain margin and fast pendulum response while the remaining two parameters, namely the pendulum and cart velocity weight factors, are maintained as free tuning parameters. The comparison of the proposed method with some optimal control methods in the absence of disturbance input shows an obvious advantage in the average peak efficiency in favor of the proposed SIMO MPC controller at the price of slightly reduced speed efficiency. Additionally, none of the compared controllers can achieve a system gain margin greater than 1.63, while the proposed one can go beyond that limit at the price of additional degradation in the speed efficiency.

Vehicle and Traffic Light Control Through Gradient-Based Coordination and Control Barrier Function Safety Regulation

In this paper we present a decentralized control framework for the coordination of connected vehicles and traffic lights in urban intersections. The framework uses gradient based methods to dynamically coordinate, at every time step, the planned intersection arrival times of vehicles and the planned switching times of traffic lights. Assuming no constraints, vehicles then use analytical optimal control methods to determine a nominal acceleration profile intended to place them at the intersection at the desired arrival time. Finally, using control barrier functions, the agents' accelerations and arrival times are modified to ensure safety and feasibility. The work in this paper builds on existing research on safe-set nonlinear control methods, multi-agent gradient based methods, and optimal control methods used to tackle the intelligent intersection management problem. Here, we integrate the use of these different approaches to present a comprehensive control architecture that can flexibly coordinate the timing of both vehicles and traffic lights, while maintaining safety and feasibility. Simulations show that the method can save between 4% to 15% in fuel consumption and between 55% to 70% in delay for different traffic conditions.

Reinforcement learning derived chemotherapeutic schedules for robust patient-specific therapy

The in-silico development of a chemotherapeutic dosing schedule for treating cancer relies upon a parameterization of a particular tumour growth model to describe the dynamics of the cancer in response to the dose of the drug. In practice, it is often prohibitively difficult to ensure the validity of patient-specific parameterizations of these models for any particular patient. As a result, sensitivities to these particular parameters can result in therapeutic dosing schedules that are optimal in principle not performing well on particular patients. In this study, we demonstrate that chemotherapeutic dosing strategies learned via reinforcement learning methods are more robust to perturbations in patient-specific parameter values than those learned via classical optimal control methods. By training a reinforcement learning agent on mean-value parameters and allowing the agent periodic access to a more easily measurable metric, relative bone marrow density, for the purpose of optimizing dose schedule while reducing drug toxicity, we are able to develop drug dosing schedules that outperform schedules learned via classical optimal control methods, even when such methods are allowed to leverage the same bone marrow measurements.

Chaos Theory Methods for Contact-Center Dinamic Control

The work is devoted to searching for optimal control methods for contact center, in particular, methods for predicting the load for further calculation of required number of operators. If the number of operators is always more than required, then the owners of the contact center will incur financial losses. If there are too few employees, the quality of service will decline. Predicting the load of the contact center is required in order to bring the optimal number of operators to work in advance. It is proposed to apply chaos theory to predict the incoming load of a contact center. Positive value of the Lyapunov index indicates the chaotic behavior of the input flow of the load. To predict the load, the methods of linear and nonlinear forecasting and the method of global approximation are used. The paper presents the results of comparing these methods for the problem of predicting the incoming load of contact center.

The Conservation of Renewable Resources

Chapter 4 further develops the theory of the conservation of living systems. Natural resource management problems are analyzed using optimal control methods. Natural resources are the state variables of the problem and management instruments are control variables. Management might include harvest, culling, restocking, reseeding, and replanting, or interventions affecting, for example, the fire regime, hydrological flows, the structure of habitats, the functioning of the system, and the ecosystem processes involved. The chapter considers three types of systems: aquatic systems, forest systems, and rangelands. It shows how the methods developed to model conversion/conservation decisions in all cases embed the Hotelling arbitrage condition. It shows how the level of conservation in each type of system is impacted by access rules, and the array of benefits obtained from the system.

Reinforcement learning derived chemotherapeutic schedules for robust patient-specific therapy

The in-silico development of a chemotherapeutic dosing schedule for treating cancer relies upon a parameterization of a particular tumour growth model to describe the dynamics of the cancer in response to the dose of the drug. In practice, it is often prohibitively difficult to ensure the validity of patient-specific parameterizations of these models for any particular patient. As a result, sensitivities to these particular parameters can result in therapeutic dosing schedules that are optimal in principle not performing well on particular patients. In this study, we demonstrate that chemotherapeutic dosing strategies learned via reinforcement learning methods are more robust to perturbations in patient-specific parameter values than those learned via classical optimal control methods. By training a reinforcement learning agent on mean-value parameters and allowing the agent periodic access to a more easily measurable metric, relative bone marrow density, for the purpose of optimizing dose schedule while reducing drug toxicity, we are able to develop drug dosing schedules that outperform schedules learned via classical optimal control methods, even when such methods are allowed to leverage the same bone marrow measurements.

An Application of Optimal Control to Sugarcane Harvesting in Thailand

The sugar industry is of great importance to the Thai economy. In general, the government sets sugarcane prices at the beginning of each harvesting season based on type (fresh or fired), sweetness (sugar content) and gross weight. The main aim of the present research is to use optimal control to find optimal sugarcane harvesting policies for fresh and fired sugarcane for the four sugarcane producing regions of Thailand, namely North, Central, East and North-east, for harvesting seasons 2012/13, 2013/14, 2014/15, 2017/18 and 2018/19. The optimality problem is to determine the harvesting policy which gives maximum profit to the farmers subject to constraints on the maximum amount that can be cut in each day, where a harvesting policy is defined as the amount of each type of sugarcane harvested and delivered to the sugar factories during each day of a harvesting season. The results from the optimal control methods are also compared with results from three optimization methods, namely bi-objective, linear programming and quasi-Newton. The results suggest that discrete optimal control is the most effective of the five methods considered. The data used in this paper were obtained from the Ministry of Industry and the Ministry of Agriculture and Co-operatives of the Royal Thai government.

An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.