scholarly journals Extending Classical Planning with State Constraints: Heuristics and Search for Optimal Planning

2018 ◽  
Vol 62 ◽  
pp. 373-431 ◽  
Author(s):  
Patrik Haslum ◽  
Franc Ivankovic ◽  
Miquel Ramirez ◽  
Dan Gordon ◽  
Sylvie Thiebaux ◽  
...  
Keyword(s):  
State Constraints ◽  
Linear Equations ◽  
Discrete Control ◽  
Optimal Planning ◽  
Ai Planning ◽  
State Variables ◽  
Power Networks ◽  
Admissible Heuristics ◽  
Classical Setting ◽  
Continuous Quantities

We present a principled way of extending a classical AI planning formalism with systems of state constraints, which relate - sometimes determine - the values of variables in each state traversed by the plan. This extension occupies an attractive middle ground between expressivity and complexity. It enables modelling a new range of problems, as well as formulating more efficient models of classical planning problems. An example of the former is planning-based control of networked physical systems - power networks, for example - in which a local, discrete control action can have global effects on continuous quantities, such as altering flows across the entire network. At the same time, our extension remains decidable as long as the satisfiability of sets of state constraints is decidable, including in the presence of numeric state variables, and we demonstrate that effective techniques for cost-optimal planning known in the classical setting - in particular, relaxation-based admissible heuristics - can be adapted to the extended formalism. In this paper, we apply our approach to constraints in the form of linear or non-linear equations over numeric state variables, but the approach is independent of the type of state constraints, as long as there exists a procedure that decides their consistency. The planner and the constraint solver interact through a well-defined, narrow interface, in which the solver requires no specialisation to the planning context.

scholarly journals Compiling Causal Theories to Successor State Axioms and STRIPS-Like Systems

2003 ◽  
Vol 19 ◽  
pp. 279-314 ◽  
Author(s):  
F. Lin
Keyword(s):  
State Constraints ◽  
Causal Theory ◽  
Situation Calculus ◽  
Formal Specifications ◽  
Ai Planning ◽  
Planning Systems ◽  
Description Language ◽  
Successor State ◽  
Action Effects ◽  
Causal Theories

We describe a system for specifying the effects of actions. Unlike those commonly used in AI planning, our system uses an action description language that allows one to specify the effects of actions using domain rules, which are state constraints that can entail new action effects from old ones. Declaratively, an action domain in our language corresponds to a nonmonotonic causal theory in the situation calculus. Procedurally, such an action domain is compiled into a set of logical theories, one for each action in the domain, from which fully instantiated successor state-like axioms and STRIPS-like systems are then generated. We expect the system to be a useful tool for knowledge engineers writing action specifications for classical AI planning systems, GOLOG systems, and other systems where formal specifications of actions are needed.

scholarly journals Static and Dynamic Portfolio Methods for Optimal Planning: An Empirical Analysis

2017 ◽  
Vol 26 (01) ◽  
pp. 1760006 ◽  
Author(s):  
Mattia Rizzini ◽  
Chris Fawcett ◽  
Mauro Vallati ◽  
Alfonso E. Gerevini ◽  
Holger H. Hoos
Keyword(s):  
Empirical Analysis ◽  
Problem Instance ◽  
Optimal Planning ◽  
Ai Planning ◽  
Wide Range ◽  
Dynamic Portfolio ◽  
Dynamic Techniques

Combining the complementary strengths of several algorithms through portfolio approaches has been demonstrated to be effective in solving a wide range of AI problems. Notably, portfolio techniques have been prominently applied to suboptimal (satisficing) AI planning. Here, we consider the construction of sequential planner portfolios for domainindependent optimal planning. Specifically, we introduce four techniques (three of which are dynamic) for per-instance planner schedule generation using problem instance features, and investigate the usefulness of a range of static and dynamic techniques for combining planners. Our extensive empirical analysis demonstrates the benefits of using static and dynamic sequential portfolios for optimal planning, and provides insights on the most suitable conditions for their fruitful exploitation.

scholarly journals A Graph Approach to Observability in Physical Sparse Linear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Santiago Vazquez-Rodriguez ◽  
Jesús Á. Gomollón ◽  
Richard J. Duro ◽  
Fernando López Peña
Keyword(s):  
Linear Systems ◽  
Equation System ◽  
The State ◽  
State Variables ◽  
Power Networks ◽  
Boundary Constraints ◽  
Linear Equation System ◽  
Electric Power Networks ◽  
Necessary And Sufficient

A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the systems. The term observability refers to the capability of estimating the state variables of a system based on the available information. In the case of linear systems, diffierent graphical approaches were developed to address this issue. In this paper a new unified graph based technique is proposed in order to determine the observability of a sparse linear physical system or, at least, a system that can be linearized after a first order derivative, using a given sensor set. A network associated to a linear equation system is introduced, which allows addressing and solving three related problems: the characterization of those cases for which algebraic and topological observability analysis return contradictory results; the characterization of a necessary and sufficient condition for topological observability; the determination of the maximum observable subsystem in case of unobservability. Two examples illustrate the developed techniques.

scholarly journals Online Speedup Learning for Optimal Planning

2012 ◽  
Vol 44 ◽  
pp. 709-755 ◽  
Author(s):  
C. Domshlak ◽  
E. Karpas ◽  
S. Markovitch
Keyword(s):  
Decision Rule ◽  
Search Space ◽  
Optimal Planning ◽  
Goal State ◽  
World State ◽  
Admissible Heuristics ◽  
State Space Search ◽  
Novel Method ◽  
Planning Task ◽  
The Cost

Domain-independent planning is one of the foundational areas in the field of Artificial Intelligence. A description of a planning task consists of an initial world state, a goal, and a set of actions for modifying the world state. The objective is to find a sequence of actions, that is, a plan, that transforms the initial world state into a goal state. In optimal planning, we are interested in finding not just a plan, but one of the cheapest plans. A prominent approach to optimal planning these days is heuristic state-space search, guided by admissible heuristic functions. Numerous admissible heuristics have been developed, each with its own strengths and weaknesses, and it is well known that there is no single "best'' heuristic for optimal planning in general. Thus, which heuristic to choose for a given planning task is a difficult question. This difficulty can be avoided by combining several heuristics, but that requires computing numerous heuristic estimates at each state, and the tradeoff between the time spent doing so and the time saved by the combined advantages of the different heuristics might be high. We present a novel method that reduces the cost of combining admissible heuristics for optimal planning, while maintaining its benefits. Using an idealized search space model, we formulate a decision rule for choosing the best heuristic to compute at each state. We then present an active online learning approach for learning a classifier with that decision rule as the target concept, and employ the learned classifier to decide which heuristic to compute at each state. We evaluate this technique empirically, and show that it substantially outperforms the standard method for combining several heuristics via their pointwise maximum.

scholarly journals Scaling industrial applications for the big data era

2021 ◽  
pp. 39-39
Author(s):  
Davor Sutic ◽  
Ervin Varga
Keyword(s):  
Power Flow ◽  
Linear Equations ◽  
Matrix Multiplication ◽  
Industrial Applications ◽  
Large Datasets ◽  
Graph Connectivity ◽  
Power Networks ◽  
Graph Sparsification ◽  
Distributed Solutions ◽  
Systems Of Linear Equations

Industrial applications tend to rely increasingly on large datasets for regular operations. In order to facilitate that need, we unite the increasingly available hardware resources with fundamental problems found in classical algorithms. We show solutions to the following problems: power flow and island detection in power networks, and the more general graph sparsification. At their core lie respectively algorithms for solving systems of linear equations, graph connectivity and matrix multiplication, and spectral sparsification of graphs, which are applicable on their own to a far greater spectrum of problems. The novelty of our approach lies in developing the first open source and distributed solutions, capable of handling large datasets. Such solutions constitute a toolkit, which, aside from the initial purpose, can be used for the development of unrelated applications and for educational purposes in the study of distributed algorithms.

scholarly journals Distribution-Based Identification of Yield Coefficients in a Baker’s Yeast Bioprocess

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
Dorin Sendrescu
Keyword(s):  
Algebraic System ◽  
Linear Equations ◽  
Distribution Theory ◽  
Baker’S Yeast ◽  
Baker's Yeast ◽  
State Variables ◽  
Algebraic Equations ◽  
Test Functions ◽  
State Equations ◽  
Unknown Parameters

A distribution-based identification procedure for estimation of yield coefficients in a baker’s yeast bioprocess is proposed. This procedure transforms a system of differential equations to a system of algebraic equations with respect to unknown parameters. The relation between the state variables is represented by functionals using techniques from distribution theory. A hierarchical structure of identification is used, which allows obtaining a linear algebraic system of equations in the unknown parameters. The coefficients of this algebraic system are functionals depending on the input and state variables evaluated through some test functions from distribution theory. First, only some state equations are evaluated throughout test functions to obtain a set of linear equations in parameters. The results of this first stage of identification are used to express other parameters by linear equations. The process is repeated until all parameters are identified. The performances of the method are analyzed by numerical simulations.

Co-Simulation of Algebraically Coupled Dynamic Subsystems Without Disclosure of Proprietary Subsystem Models

2004 ◽  
Vol 126 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Bei Gu ◽  
H. Harry Asada
Keyword(s):  
Sliding Mode ◽  
Linear Equations ◽  
Numerical Data ◽  
Stability And Convergence ◽  
State Variables ◽  
Differential Algebraic Equation ◽  
Dynamic Interactions ◽  
Boundary Constraints ◽  
Nonlinear Control Theory ◽  
Systematic Solution

A method for simultaneously running a collection of dynamic simulators coupled by algebraic boundary conditions is presented. Dynamic interactions between subsystems are simulated without disclosing proprietary information about the subsystem models, as all the computations are performed based on input-output numerical data of encapsulated subsystem simulators coded by independent groups. First, this paper describes a system of interacting subsystems with a causal conflict as a high-index, Differential-Algebraic Equation (DAE), and develops a systematic solution method using Discrete-Time Sliding Mode control. Stability and convergence conditions as well as error bounds are analyzed by using nonlinear control theory. Second, the algorithm is modified such that the subsystem simulator does not have to disclose its internal model and state variables for solving the overall DAE. The new algorithm is developed based on the generalized Kirchhoff Laws that allow us to represent algebraic boundary constraints as linear equations of the subsystems’ outputs interacting to each other. Third, a multi-rate algorithm is developed for improving efficiency, accuracy, and convergence characteristics. Numerical examples verify the major theoretical results and illustrate features of the proposed method.

scholarly journals New Islands of Tractability of Cost-Optimal Planning

2008 ◽  
Vol 32 ◽  
pp. 203-288 ◽  
Author(s):  
M. Katz ◽  
C. Domshlak
Keyword(s):  
Constructive Proof ◽  
Optimal Planning ◽  
Constraint Optimization ◽  
State Variables ◽  
Proof Technique ◽  
Causal Graph ◽  
Intractable Problems ◽  
Causal Graphs ◽  
Almost All ◽  
Planning Problems

We study the complexity of cost-optimal classical planning over propositional state variables and unary-effect actions. We discover novel problem fragments for which such optimization is tractable, and identify certain conditions that differentiate between tractable and intractable problems. These results are based on exploiting both structural and syntactic characteristics of planning problems. Specifically, following Brafman and Domshlak (2003), we relate the complexity of planning and the topology of the causal graph. The main results correspond to tractability of cost-optimal planning for propositional problems with polytree causal graphs that either have O(1)-bounded in-degree, or are induced by actions having at most one prevail condition each. Almost all our tractability results are based on a constructive proof technique that connects between certain tools from planning and tractable constraint optimization, and we believe this technique is of interest on its own due to a clear evidence for its robustness.

scholarly journals Energy Space Modeling of Power Electronics in Local Area Power Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Gregory M. Vosters ◽  
Wayne W. Weaver
Keyword(s):  
Power Electronics ◽  
Control Strategies ◽  
Local Area ◽  
Energy Utilization ◽  
State Variables ◽  
Level Control ◽  
Power Networks ◽  
Change Of Variables ◽  
Space Modeling ◽  
High Level

Power electronics are a core enabling technology for local area power networks and microgrids for renewable energy, telecom, data centers, and many other applications. Unfortunately, the modeling, simulation, and control of power electronics in these systems are complicated when using traditional converter models in conjunction with the network nodal equations. This work proposes a change of variables for the power electronic converter models from traditional voltage and currents to input conductance and stored energy. From this change of state, a universal point of load converter model can be utilized in the network nodal equations irrespective of the topology of the converter. The only impact the original converter topology has on the new model is the bounds on the control and state variables, and the mapping back to the switching or duty cycle controls. The proposed approach greatly simplifies the modeling of local area power networks and microgrids. This simpler model can be used to study stability and energy utilization and develop high-level control strategies that were not previously feasible.

scholarly journals Multi-Criteria Optimisation of Multi-Stage Positional Game of Vessels

2020 ◽  
Vol 27 (1) ◽  
pp. 46-52
Author(s):  
Józef Lisowski
Keyword(s):  
Mathematical Model ◽  
State Constraints ◽  
Control Algorithms ◽  
State Variables ◽  
The North ◽  
Positional Games ◽  
Multi Stage ◽  
The North Sea ◽  
Safe Control ◽  
Control State

AbstractThe paper presents a mathematical model of a positional game of the safe control of a vessel in collision situations at sea, containing a description of control, state variables and state constraints as well as sets of acceptable ship strategies, as a multi-criteria optimisation task. The three possible tasks of multi-criteria optimisation were formulated in the form of non-cooperative and cooperative multi-stage positional games as well as optimal non-game controls. The multi-criteria control algorithms corresponding to these tasks were subjected to computer simulation in Matlab/Simulink software based on the example of the real navigational situation of the passing of one’s own vessel with eighteen objects encountered in the North Sea.

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