State In Minimum Time Research Articles

Minimum-time strategy optimization for networked evolutionary games with bankruptcy mechanism

In this paper, the minimum-time strategy optimization problem for NEGs with bankruptcy mechanism is considered based on semi-tensor product of matrices. Firstly, in order to describe the impact of bankruptcy mechanism on evolution, a novel matrix called controlled state transition matrix is constructed by deleting all invalid states, which will also reduce the computational complexity of subsequent analysis and design. Secondly, by assorting to the redefined matrix, the minimum-time strategy optimization problem for NEGs with bankruptcy mechanism can be solved by designing state feedback control which can guarantee the convergence of states without violating the bankruptcy mechanism. Meanwhile, the verification condition is derived to verify the existence of the state feedback control, and an algorithm for seeking all possible minimum-time state feedback controllers is constructed. Finally, a typical example is illustrated to validate the effectiveness of the proposed method.

Influence of quantity of additional food in achieving biological conservation and pest management in minimum-time for prey-predator systems involving Holling type III response

Incorporating additional food supplements into the predators' diet complementary to the target prey has gained importance over the years due to its pertinence in achieving biological conservation and biological control. Studies by theoretical ecologists and mathematicians reveal that by providing appropriate quality and quantity of additional food to the predator, the system could be driven either towards co-existence of species (to an admissible interior equilibrium), thereby achieving conservation or towards elimination of either of species achieving bio-control eventually with time. However, one of the limitations of these studies is that the desired state is reached only as asymptotes which makes the outcomes of the studies not that practically viable. In this work, to overcome the limitation of asymptotes, we formulate and study a time optimal control problem for additional food provided system involving type III response using quantity of additional food as the control. The objective of the study is to reach the desired terminal state in minimum time. To that end, we first prove the existence of optimal solution using the Filippov's existence theorem and then establish the characteristics of the optimal control using the Pontryagin's Maximum Principle. Using the Hamiltonian minimization condition and the monotonicity property of the Hamiltonian with respect to the quantity parameter, we show that the optimal control strategy is of bang-bang type with a possibility of multiple switches in the trajectory in case of biological conservation and no switch in case of pest management. Since the additional food system exhibits contrasting behaviour with respect to quality additional food, we have considered multiple cases of quality as a part of this study and in each case, we fixed the quality parameter as constant. The theoretical results have been illustrated by performing numerical simulations for various cases relating to both biological conservation and pest management. The theoretical outcomes of this study are in line with ecological field observations.

A shortcut tour of quantum control methods for modern quantum technologies

Quantum control methods, like rapid adiabatic passage, stimulated Raman adiabatic passage, shortcuts to adiabaticity and optimal control, have become an integral part of modern quantum technologies, for example quantum computation and sensing, where they are exploited in order to find the optimal pulse sequences which drive quantum systems to the desired target state in minimum time or with maximum fidelity, overcoming decoherence and dissipation. In this perspective, we use the basic example of adiabatic population inversion in a two-level system in order to present these methods and review the latest developments in the field, while we touch upon the emerging method of reinforcement learning.

Time optimal control of two-level quantum systems

The objective of time-optimal control that helps to minimize relaxation losses, is the evolution of a quantum state from a given initial mixed state to a final target mixed state in minimum time. In this paper, we study a time-optimal control problem of the dynamic of a pure two-level system with unbounded control using Pontryagin's minimum principle and obtain the minimal time for some initial and final states. The results will apply to basically all qubit systems that one can consider such as NMR spectroscopy, trapped ions, superconducting qubits, etc. We also show that these results hold for pure states, and only the direction nˆ is important in the evolution of a quantum state. In this work, the problem of computing minimum time to produce any unitary transformation Uf∈SU(2) is reduced to finding the minimum time to steer the system from an initial to a final state.

Minimum time state consensus for cooperative attack of multi-missile systems

This paper considers the cooperative attack with multiple missiles on a stationary target and a two-step procedure is proposed. First the states of all missiles are guided to achieve minimum time consensus, and then, by using the proportional navigation guidance law with identical navigation gain each missile arrives at the target simultaneously or sequentially. Among which, the strategy to realize state consensus in minimum time is the focus of the issue. In the paper the coordination algorithms are developed based on bang–bang control strategy due to its simply structure, subsequently, it is proved that the time optimal consensus problem can be transformed into a parameter optimization problem. Besides, the proposed schemes are able to significantly reduce the number of parameters to be optimized and finally solve the problem with little computation cost. Different from the impact time control methods, the strategy for state consensus does not demand the information of time-to-go. Meanwhile only the initial values of missiles' states are required for the coordination algorithms which lead to less communication burden. Two different examples are provided to demonstrate the validity and efficiency of our proposed strategy.

A Leukocyte Detection Technique in Blood Smear Images Using Plant Growth Simulation Algorithm

For quite some time, the analysis of leukocyte images has drawn significant attention from the fields of medicine and computer vision alike where various techniques have been used to automate the manual analysis and classification of such images. Analysing such samples manually for detecting leukocytes is time-consuming and prone to error as the cells have different morphological features. Therefore, in order to automate and optimize the process, the nature-inspired Plant Growth Simulation Algorithm (PGSA) has been applied in this paper. An automated detection technique of white blood cells embedded in obscured, stained and smeared images of blood samples has been presented in this paper which is based on a random bionic algorithm and makes use of a fitness function that measures the similarity of the generated candidate solution to an actual leukocyte. As the proposed algorithm proceeds the set of candidate solutions evolves, guaranteeing their fit with the actual leukocytes outlined in the edge map of the image. The experimental results of the stained images and the empirical results reported validate the higher precision and sensitivity of the proposed method than the existing methods. Further, the proposed method reduces the feasible sets of candidate points in each iteration, thereby decreasing the required run time of load flow, objective function evaluation, thus reaching the goal state in minimum time and within the desired constraints.

An object localization optimization technique in medical images using plant growth simulation algorithm.

The analysis of leukocyte images has drawn interest from fields of both medicine and computer vision for quite some time where different techniques have been applied to automate the process of manual analysis and classification of such images. Manual analysis of blood samples to identify leukocytes is time-consuming and susceptible to error due to the different morphological features of the cells. In this article, the nature-inspired plant growth simulation algorithm has been applied to optimize the image processing technique of object localization of medical images of leukocytes. This paper presents a random bionic algorithm for the automated detection of white blood cells embedded in cluttered smear and stained images of blood samples that uses a fitness function that matches the resemblances of the generated candidate solution to an actual leukocyte. The set of candidate solutions evolves via successive iterations as the proposed algorithm proceeds, guaranteeing their fit with the actual leukocytes outlined in the edge map of the image. The higher precision and sensitivity of the proposed scheme from the existing methods is validated with the experimental results of blood cell images. The proposed method reduces the feasible sets of growth points in each iteration, thereby reducing the required run time of load flow, objective function evaluation, thus reaching the goal state in minimum time and within the desired constraints.

Light-based circadian rhythm control: Entrainment and optimization

Light is a strong synchronizer for circadian rhythm — the 24-h biological oscillation in plants, insects, and mammals. This paper considers the circadian entrainment problem for a popular circadian oscillation model (the Kronauer model) by using light intensity as the control input. This problem is commonly encountered by shift workers and international travelers — how to shift the phase of one’s circadian rhythm by a specified amount, preferably as fast as possible? We consider three approaches: 1. Periodic entrainment: use the light/dark cycle corresponding to the desired circadian rhythm as the light input. 2. Optimal entrainment: use light input to shift the circadian rhythm to the desired state in minimum time. 3. Feedback entrainment: use circadian state feedback to adjust light input. For feedback entrainment, we consider two cases: active lighting control which can inject artificial lighting on demand and subtractive lighting control which only blocks the ambient lighting. For the periodic entrainment, which is used as a baseline for comparison, we apply the harmonic balance method to assess the existence of a stable periodic solution, and verify the result by simulation. For the minimum time entrainment, we present an efficient solution to the two-point boundary value problem and show that active lighting control significantly reduces the entrainment time from the baseline. The feedback algorithm augments the periodic entrainment with a circadian state feedback to account for modeling error and noise. Results from this study provide new insight and guideline to light intensity control for circadian rhythm regulation.

Analysis of the Buck Converter for Scaling the Supply Voltage of Digital Circuits

The energy consumption in mobile systems has become a big challenge that limits high performance and autonomy in mobile systems. The dynamic voltage scaling (DVS) is a recent technique that reduces energy consumption varying dynamically the supply voltage of the system accordingly to the clock frequency. The Buck topology is a good candidate to supply step variations of the output voltage meeting the DVS requirements. In this paper, it is analyzed which is the fastest output voltage evolution that can provide the Buck topology. The minimum time state transition in the Buck converter and its corresponding control law are obtained applying the Maximum Principle or Pontryagin's Principle. Design criteria for the Buck topology are derived from this result. The analysis is extended to a multiphase Buck converter. The minimum time control law is validated in a prototype. The measurements are in good agreement with the theoretical results.

Dead-beat control of simple Hammerstein models

Dead-beat controllers for simple Hammerstein systems are investigated. Several designs for nonminimum-time state dead-beat controllers are given for certain classes of simple Hammerstein systems. A general minimum-time state dead-beat controller is presented for a class of simple Hammerstein systems. A design for a family of minimum-time control laws is provided. This enables, to a certain extent, shaping of transient response via choosing an appropriate control law. Finally, the authors design an output dead-beat controller for a class of Hammerstein systems that are not necessarily state dead-beat controllable.

Feedback control of minimum‐time optimal control problems using neural networks

AbstractThis paper presents an optimal feedback controller capable of driving a non‐linear control system from an arbitrary initial state to a fixed final state in minimum time. The controller is based on a feedforward multilayer neural network trained repeatedly using open‐loop optimal control data which densely span the field of extremals of the non‐linear system. The effectiveness of the controller is clearly demonstrated by a simulation on a two‐link robot manipulator. The effect of sensor/actuator noise and parameter variation is also included to confirm the robustness of the controller.

Time-optimal decoupling control problems

This paper treats the problem of time-optimal decoupled control for multi-input multi-output systems subject to constraints on the controls. The problem is to determine a control vector which transfers one state variable from a given initial steady state to a given final steady state in minimum time, whilst holding the remaining state variables constant. The solution is obtained using an extension of Pontryagin's maximum principle to problems in which the state-control space is subject to additional non-differential inequality constraints. By an appropriate reformulation of the problem it is shown that the optimal solution requires that one of the controls be set at its extreme (saturated) value, while the other controls arc determined from the constraints on the state variables which are held constant. The controls behave continuously without switching, but the choice of the control which is held at saturation is changed at certain points. The optimal solutions are easily represented by phase-plane diagr...

On Feedback Laws for Robotic Systems

Abstract : A variety of control problems arising from robotics applications can be restated as optimal control problems of minimum-time state transfer in the presence of state-space constraints and constraints of incomplete-state information. The traditional approaches to solving such problems are Pontryagin's Maximum Principle, in the case of open-loop control, and Bellman's Dynamic Programming method.

Minimum time controllers of linear discrete-time systems

This paper deals with the minimum time state regulation problem of finite-dimensional linear time-invariant discrete-time systems in the case where the information of the initial state in some linear space is available. The information can be effectively used to regulate the system fast. In this case, the minimum time controller with time-varying coefficients regulates the system faster than the one with time-invariant coefficients in general.

Rosenbrock's theorem and the minimum time state regulator problem

Rosenbrock's theorem is used to give a clear and efficient solution to the (discrete-time) minimum time state regulator problem. It is shown that the optimal feedback gain can be naturally computed using already existing algorithms. A further result related to Rosenbrock's theorem is also given.

Observer design for the minimum-time state reconstruction of linear discrete-time systems

Observer design for the minimum-time state reconstruction of linear discrete-time systems

Observer Design for the Minimum-Time State Reconstruction of Linear Discrete-Time Systems

The problem of observer design for the minimum-time state reconstruction of a general class of discrete-time linear multivariable systems is considered. Both full-order and minimal-order observers, each specified by a gain matrix in closed form, are presented which reconstruct the system state in a minimum of vo and vo − 1 steps respectively, where vo is the system observability index. The simplicity and generality of the designs are demonstrated by numerical example.

On time optimal control of linear discrete-time systems by geometric approach

This paper arose from the need for a better understanding of the minimum time state regulation problem of finite-dimensional linear time-invariant discrete systems with an incomplete state observation. For this we used a geometric approach and obtained the following interesting results. First, the necessary and sufficient condition of the existence of controllers which regulate the system from any initial state to the origin in finite steps is that the system is controllable and reconstructable. Secondly, the general minimum regulation time is obtained, which is the maximum value of the minimum regulation time. Thirdly, two typical controllers which drive the system from any initial state to the origin in the general minimum regulation time are designed. One is a time-variant system taking the system's input and output of each time as input. The other is a time-invariant system. Fourthly, it is shown that the controller does not necessarily exist which transfers the system to the origin in the minimum reg...

Improvement of transient stability problem for the A.R.E. 500 KV ties using optimal control

Transient stability problem for the Aswan Area against infinite bus equivalent system is investigated. In this equivalent system, the Aswan hydro station(10 units) is simulated by an equivalent machine connected through 500 KV transmission lines to Cairo Area. The study is carried out for three phase faults with successful reclosure at different locations. Then, the transient stability of the system is improved for those cases using intermittent switching of two series capacitors, that is, bang-bang control of line reactance. The power system is then restored to its initial steady state in minimum time after a transient disturbance in non oscillatory manner. With that technique, stability of the system is maintained for some cases that show great instability without that control. This problem is identified as a minimum time one in optimal control theory.

Two-step procedure for time-suboptimal control

Abstract A two-step procedure for stable time-suboptimal control is proposed. The procedure involves the use of two feedback gain matrices. The first matrix is determined to transfer the system from a given state to the vicinity of the desired state in minimum time. Then a switch is made to a second feedback gain matrix obtained from shifting of eigenvalues For maximum stability. The viability of the proposed procedure is demonstrated with a linear six-p!ate gas absorber and a non-linear two-stage CSTR system.