Time-dependent Constraints Research Articles

Cournot Maps for Intercepting Evader Evolutions by a Pursuer

Instead of studying evolutions governed by an evolutionary system starting at a given initial state on a prescribed future time interval, finite or infinite, we tackle the problem of looking both for a past interval $$[T-D,T]$$ of duration D and for the viable evolutions arriving at a prescribed terminal state at the end of the temporal window (and thus telescoping if more than one such evolutions exist). Hence, given time-duration dependent evolutionary system and viability constraints, as well as time dependent departure constraints, the Cournot map associates with any terminal time $$T$$ and state $$x$$ the durations $$D(T,x)$$ of the intervals $$[T-D(T,x),T]$$ , the starting (or initial) states at the beginning of the temporal window from which at least one viable evolution will reach the given terminal state $$x$$ at $$T$$ . Cournot maps can be used by a Pursuer to intercept an evader’s evolution in dynamic game theory. After providing some properties of Cournot maps are next investigated, above all, the regulation map piloting the viable evolutions at each time and for each duration from the beginning of the temporal window up to terminal time. The next question investigated is the selection of controls or regulons in the regulation map whenever several of them exist. Selection processes are either time dependent, when the selection operates at each time, duration, and state for selecting a regulon satisfying required properties (for instance, minimal norm, minimal speed), or intertemporal. In this case, viable evolutions are required to optimize some prescribed intertemporal functional, as in optimal control. This generates value functions, the topics of the second part of this study. An example is provided: the Pursuer is a security vehicle making the rounds along a predetermined path, the departure tube, for reaching any network location where and when alarms sound to signal the location (of the evader). The software of the Cournot algorithm computes the minimal duration and the moment when the Pursuer leaves its round to reach the detected location as soon as possible and how to proceed by embedding in the Pursuer system the graph of the feedback map governing the evolution of the Pursuer vehicle.

General-Weighted Least-Norm Control for Redundant Manipulators under Time-Dependent Constraint

Previous research dealing with constrained kinematic redundancy problems focuses on manipulators with time-independent constraints. This paper extends the general-weighted least-norm (GWLN) method to manipulators with time-dependent constraints by introducing time-dependent virtual joints. In the virtual joint space, corresponding task space velocity is revised to encapsulate the effects of time-dependent parameters of constraints. This is done so that an intermediate kinematic control problem with only joint limit is obtained. Then, the inverse kinematic problem is solved in the virtual joint space. A new inverse-weighted matrix setting criterion is proposed to replace the one-step prediction that originally complicated implementation of the GWLN method. To demonstrate the efficacy of the method, simulations and experiments are carried out on a five-link welding manipulator to track the welding trajectory. Time-dependent orientation constraint and preventing joint limits is guaranteed using this method.

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

We consider the parallel-machine scheduling problem in which the machines have availability constraints and the processing time of each job is simple linear increasing function of its starting times. For the makespan minimization problem, which is NP-hard in the strong sense, we discuss the Longest Deteriorating Rate algorithm and List Scheduling algorithm; we also provide a lower bound of any optimal schedule. For the total completion time minimization problem, we analyze the strong NP-hardness, and we present a dynamic programming algorithm and a fully polynomial time approximation scheme for the two-machine problem. Furthermore, we extended the dynamic programming algorithm to the total weighted completion time minimization problem.

Existence and approximation for vibro-impact problems with a time-dependent set of constraints

We consider a discrete mechanical system subjected to perfect time-dependent unilateral constraints, which dynamics is described by a second order measure differential inclusion. The transmission of the velocity at impacts is given by a minimization property of the kinetic energy with respect to the set of kinematically admissible post-impact velocities. We construct a sequence of feasible approximate positions by using a time-stepping algorithm inspired by a kind of Euler discretization of the differential inclusion. We prove the convergence of the approximate trajectories to a solution of the Cauchy problem and we obtain as a by-product a global existence result.

Multi-objective Weather Routing with Customised Criteria and Constraints

The paper presents a weather routing algorithm utilising a multi-objective optimisation with constraints, namely the Multi-objective Evolutionary Weather Routing Algorithm (MEWRA). In the proposed approach weather route recommendations can be made simultaneously e.g. for passage time, fuel consumption and safety of passage by means of Pareto optimisation. The sets of criteria and constraints in the optimisation process are fully customisable. The algorithm handles static (time-independent) and dynamic (time-dependent) constraints e.g. forecasted high wind speed regions or customisable areas to be excluded from routing (e.g. due to piracy). The paper includes a description of MEWRA as well as examples of its usage for finding Pareto-optimal transoceanic ship routes.

Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints

Abstract In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized differential-algebraic equations with non-autonomous constraints of a particular type. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions of the considered equations. Our approach is based on topological arguments as regards differential equations on implicitly defined manifolds, combined with elementary facts of matrix analysis. MSC: 34A09, 34C25, 34C40.

Rate-Independent Dynamics and Kramers-Type Phase Transitions in Nonlocal Fokker–Planck Equations with Dynamical Control

The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker–Planck equations that involve two small parameters and are driven by a time-dependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and show that the dynamics in the small-parameter limit can be described by a rate-independent evolution equation with hysteresis. For the proof we first derive mass-dissipation estimates by means of Muckenhoupt constants, formulate conditional stability estimates, and characterize the mass flux between the different phases in terms of moment estimates that encode large deviation results. Afterwards we combine all these partial results and establish the dynamical stability of localized peaks as well as sufficiently strong compactness results for the basic macroscopic quantities.

Rule-based peer-to-peer framework for decentralised real-time service oriented architectures

Modularity has been a key issue in the design and development of modern embedded Real-Time Software Systems (RTS) where modularity enables flexibility with respect to changes in platform, environment, and requirements, as well as reuse. In distributed RTS, similar ideas have led to the adoption of Commercial Off-The-Shelf (COTS) components integrated via Service-Oriented Architecture (SOA) principles and technologies that are already well-established in business-oriented information systems. However, current SOA technologies for orchestration, such as Enterprise Service Busses, do not meet strict time-dependent constraints on scalability and latency required by RTS.We present a novel approach to RTS development where the orchestration of real-time processes is decentralised among the services within a fully distributed rule-driven process framework. Our framework wraps around COTS components implementing individual processing steps in a decentralised real-time process. Our execution model incorporates real-time constraints and is configurable through message routing policies distributed as a knowledge base containing rule sets, and therefore dispenses with the need for a central orchestration component which could easily become a bottleneck. Deterministic behaviour can be achieved through the validation of the rule-sets and the use of Modular Performance Analysis (MPA).We analyse the performance of our architecture using the Real-Time Calculus and show by empirical evaluation that our method scales to a typical real-time process application found in a tactical naval combat system context.

Global existence for a nonlocal and nonlinear Fokker–Planck equation

We consider a Fokker–Planck equation on a compact interval where, as a constraint, the first moment is a prescribed function of time. Eliminating the associated Lagrange multiplier, one obtains nonlinear and nonlocal terms. After establishing suitable local existence results, we use the relative entropy as an energy functional. However, the time-dependent constraint leads to a source term such that a delicate analysis is needed to show that the dissipation terms are strong enough to control the work done by the constraint. We obtain global existence of solutions as long as the prescribed first moment stays in the interior of an interval. If the prescribed moment converges to a constant value inside the interior of the interval, then the solution stabilises to the unique steady state.

Periodic-Zone Model Predictive Control for Diurnal Closed-Loop Operation of an Artificial Pancreas

The objective of this research is an artificial pancreas (AP) that performs automatic regulation of blood glucose levels in people with type 1 diabetes mellitus. This article describes a control strategy that performs algorithmic insulin dosing for maintaining safe blood glucose levels over prolonged, overnight periods of time and furthermore was designed with outpatient, multiday deployment in mind. Of particular concern is the prevention of nocturnal hypoglycemia, because during sleep, subjects cannot monitor themselves and may not respond to alarms. An AP intended for prolonged and unsupervised outpatient deployment must strategically reduce the risk of hypoglycemia during times of sleep, without requiring user interaction. A diurnal insulin delivery strategy based on predictive control methods is proposed. The so-called "periodic-zone model predictive control" (PZMPC) strategy employs periodically time-dependent blood glucose output target zones and furthermore enforces periodically time-dependent insulin input constraints to modulate its behavior based on the time of day. The proposed strategy was evaluated through an extensive simulation-based study and a preliminary clinical trial. Results indicate that the proposed method delivers insulin more conservatively during nighttime than during daytime while maintaining safe blood glucose levels at all times. In clinical trials, the proposed strategy delivered 77% of the amount of insulin delivered by a time-invariant control strategy; specifically, it delivered on average 1.23 U below, compared with 0.31 U above, the nominal basal rate overnight while maintaining comparable, and safe, blood glucose values. The proposed PZMPC algorithm strategically prevents nocturnal hypoglycemia and is considered a significant step toward deploying APs into outpatient environments for extended periods of time in full closed-loop operation.

조속기의 동적 평형위치 해석

Abstract This paper proposes a method to obtain the dynamic equilibrium configuration of a constrained mechanical system by using multibody dynamic analysis. Dynamic equilibrium equations with independent coordinates are derived from the time-dependent constraint equations and dynamic equations of a multibody system. The Newton–Raphson method is used to find numerical solutions for nonlinear algebraic equations that are composed of the dynamic equilibrium and constraint equations. The proposed method is applied to obtain the dynamic equilibrium configuration of a speed governor, and the results are verified on the basis of the results from conventional dynamic analysis. Furthermore, vertical displacements at equilibrium configuration, which varied with the rotational velocity of the speed governor, are calculated, and design parameter analysis of the equilibrium configuration is presented. Key Words : dynamic equilibrium configuration, constrained mechanical system, multibody dynamic analysis, speed governor

Multi-agent orienteering problem with time-dependent capacity constraints

In this paper, we formulate and study the Multi-agent Orienteering Problem with Time-dependent Capacity Constraints (MOPTCC). MOPTCC is similar to the classical orienteering problem at the single-agent level: given a limited time budget, an agent travels around the network and collects rewards by visiting different nodes, with the objective of maximizing the sum of his collected rewards. The most important feature we introduce in MOPTCC is the inclusion of multiple competing and interacting agents. All agents in MOPTCC are assumed to be self-interested, and they interact with each other when arrive at the same nodes simultaneously. As all nodes are capacitated, if a particular node receives more agents than its capacity, all agents at that node will be made to wait and agents suffer collectively as a result (in terms of extra time needed for queueing). Due to the decentralized nature of the problem, MOPTCC cannot be solved in a centralized manner; instead, we need to seek out equilibrium solutions; and if this is not possible, at least approximated equilibrium solutions. The major contribution of this paper is the formulation of the problem, and our first attempt in identifying an efficient and effective equilibrium-seeking procedure for MOPTCC.

Employing UML and OCL for designing and analysing role-based access control

The stringent security requirements of organisations like banks or hospitals frequently adopt role-based access control (RBAC) principles to represent and simplify their internal permission management. While representing a fundamental advanced RBAC concept enabling precise restrictions on access rights, authorisation constraints increase the complexity of the resulting security policies so that tool support for convenient creation and adequate validation is required. A particular contribution of our work is a new approach to developing and analysing RBAC policies using a UML-based domain-specific language (DSL), which allows the hiding of the mathematical structures of the underlying authorisation constraints implemented in OCL. The DSL we present is highly configurable and extensible with respect to new concepts and classes of authorisation constraints, and allows the developer to validate RBAC policies in an effective way. The handling of dynamic (that is, time-dependent) constraints, their visual representation through the RBAC DSL and their analysis all form another part of our contribution. The approach is supported by a UML and OCL validation tool.

Optimal motion planning of redundant manipulators with controlled task infeasibility

In optimal motion planning and control, the complex time-varying nature of redundant robots, environments, and task requirements causes complex domains and conflicting constraints. Since predicting or recovering infeasibility is not always possible, infeasibilities occur frequently and are not completely avoidable. We introduce a constrained nonlinear programming framework of controlled (as opposed to recovered) infeasibility for physically valid solutions while preserving the original problem and variable space. The constraint prioritization hierarchy includes a comprehensive classification of physical consistency, design requirements, and tasks. Priority weight functions having features of normalization and prioritization are incorporated into a sequential quadratic programming (SQP) algorithm to ensure generality and strict satisfaction of high-priority constraints, while lower-priority constraint violations are minimized. These are embedded in SQP through its merit function and composite cost function, in which general nonlinear functions including unilateral, time-dependent, and nonholonomic, can be incorporated in a unified approach. Also, the avoidance of the discontinuity problem with unilateral constraints is due to the time-dependent constraints strategy, which actively adapts to varying states. Numerical examples using multibody dynamic models of a redundant manipulator demonstrate these advantages.

Generalized Kuhn--Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources

In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with $N$ firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding social planner optimal policy. Our conditions are a stochastic infinite-dimensional generalization of the Kuhn--Tucker theorem. The Lagrange multiplier takes the form of a nonnegative optional random measure on $[0,T]$ which is flat off the set of times for which the constraint is binding, i.e., when all the fuel is spent. As a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in Bank [SIAM J. Control Optim., 44 (2005), pp. 1529--1541]. In the infinite-horizon case, with operating profit functions of Cobb--Douglas type, our method allows the explicit calculation of t...

A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization

A primary concern in practical engineering design is ensuring high system reliability throughout a product's lifecycle, which is subject to time-variant operating conditions and component deteriorations. Thus, the capability of dealing with time-dependent probabilistic constraints in reliability-based design optimization (RBDO) is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. This approach employs the kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization (EGO) technique is integrated with the NERS approach to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation (ARPMM) mechanism is developed based on the mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis, and existing advanced reliability analysis and design methods can be used. The NERS approach is compared with existing time-dependent reliability analysis approaches and integrated with RBDO for engineered system design with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

Linear time-dependent constraints programming with MSVL

This paper investigates specifying and solving linear time-dependent constraints with an interval temporal logic programming language MSVL. To this end, linear constraint statements involving linear equality and non-strict inequality are first defined. Further, the time-dependent relations in the constraints are specified by temporal operators, such as [InlineEquation not available: see fulltext.]. Thus, linear time-dependent constraints can be smoothly incorporated into MSVL. Moreover, to solve the linear constraints within MSVL by means of reduction, the operational semantics for linear constraints is given. In particular, semantic equivalence rules and transition rules within a state are presented, which enable us to reduce linear equations, inequalities and optimization problems in a convenient way. Besides, the operational semantics is proved to be sound. Finally, a production scheduling application is provided to illustrate how our approach works in practice.

The Cahn–Hilliard equation with time-dependent constraint

We propose an abstract variational inequality formulation of the Cahn–Hilliard equation with a time-dependent constraint. We introduce notions of strong and weak solutions, and prove that a strong solution, if it exists, is a weak solution, and that the existence of a unique weak solution holds under an appropriate time-dependence condition on the constraint. We also show that the weak solution is a strong solution under appropriate assumptions on the data. Our abstract results can be applied to various concrete problems.

Controllable C1 continuous blending of time-dependent parametric surfaces

This paper proposes the concept of blending time-dependent varying surfaces, and develops a new method to create a controllable C1 continuous blending surface between primary parametric surfaces whose position and shape change with time. We treat it as a boundary-valued problem defined by the mathematical model of a vectored dynamic fourth-order partial differential equation subjected to time-dependent C1 continuous blending boundary constraints. High performance blending surface generation is achieved through the development of an approximate analytical solution of the mathematical model. We investigate the accuracy and efficiency of the solution, study the effective shape control of the blending surfaces, and apply the obtained solution to tackle surface blending problems. The applications demonstrate that our proposed approach is very effective and efficient in dealing with controllable C1 continuous surface blending between time-dependent varying parametric surfaces.

845 零空間法の拡張と拘束条件が時間に依存する場合への適用

845 零空間法の拡張と拘束条件が時間に依存する場合への適用