scholarly journals A Heuristic Search Approach to Planning with Continuous Resources in Stochastic Domains

2009 ◽  
Vol 34 ◽  
pp. 27-59 ◽  
Author(s):  
N. Meuleau ◽  
E. Benazera ◽  
R. I. Brafman ◽  
E. A. Hansen ◽  
Mausam
Keyword(s):  
State Space ◽  
Heuristic Search ◽  
Resource Constraints ◽  
Computational Effort ◽  
The State ◽  
Continuous Variables ◽  
State Variables ◽  
Heuristic Search Algorithms ◽  
Continuous State ◽  
Stochastic Domains

We consider the problem of optimal planning in stochastic domains with resource constraints, where the resources are continuous and the choice of action at each step depends on resource availability. We introduce the HAO* algorithm, a generalization of the AO* algorithm that performs search in a hybrid state space that is modeled using both discrete and continuous state variables, where the continuous variables represent monotonic resources. Like other heuristic search algorithms, HAO* leverages knowledge of the start state and an admissible heuristic to focus computational effort on those parts of the state space that could be reached from the start state by following an optimal policy. We show that this approach is especially effective when resource constraints limit how much of the state space is reachable. Experimental results demonstrate its effectiveness in the domain that motivates our research: automated planning for planetary exploration rovers.

scholarly journals Goal Probability Analysis in Probabilistic Planning: Exploring and Enhancing the State of the Art

2016 ◽  
Vol 57 ◽  
pp. 229-271 ◽  
Author(s):  
Marcel Steinmetz ◽  
Jörg Hoffmann ◽  
Olivier Buffet
Keyword(s):  
Heuristic Search ◽  
Resource Constraints ◽  
State Of The Art ◽  
Search Algorithm ◽  
Search Algorithms ◽  
The State ◽  
Probabilistic Planning ◽  
Large Space ◽  
Heuristic Search Algorithms ◽  
Wide Range

Unavoidable dead-ends are common in many probabilistic planning problems, e.g. when actions may fail or when operating under resource constraints. An important objective in such settings is MaxProb, determining the maximal probability with which the goal can be reached, and a policy achieving that probability. Yet algorithms for MaxProb probabilistic planning are severely underexplored, to the extent that there is scant evidence of what the empirical state of the art actually is. We close this gap with a comprehensive empirical analysis. We design and explore a large space of heuristic search algorithms, systematizing known algorithms and contributing several new algorithm variants. We consider MaxProb, as well as weaker objectives that we baptize AtLeastProb (requiring to achieve a given goal probabilty threshold) and ApproxProb (requiring to compute the maximum goal probability up to a given accuracy). We explore both the general case where there may be 0-reward cycles, and the practically relevant special case of acyclic planning, such as planning with a limited action-cost budget. We design suitable termination criteria, search algorithm variants, dead-end pruning methods using classical planning heuristics, and node selection strategies. We design a benchmark suite comprising more than 1000 instances adapted from the IPPC, resource-constrained planning, and simulated penetration testing. Our evaluation clarifies the state of the art, characterizes the behavior of a wide range of heuristic search algorithms, and demonstrates significant benefits of our new algorithm variants.

scholarly journals A Stochastic and State Space Model for Tumour Growth and Applications

2009 ◽  
Vol 10 (2) ◽  
pp. 117-138 ◽  
Author(s):  
Wai-Yuan Tan ◽  
Weiming Ke ◽  
G. Webb
Keyword(s):  
State Space ◽  
Stochastic System ◽  
Tumour Growth ◽  
Deterministic Model ◽  
State Space Model ◽  
Tumour Cells ◽  
The State ◽  
System Model ◽  
State Variables ◽  
Space Model

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

A State Space Method for Optimal Design of Vibration Isolators

1979 ◽  
Vol 101 (2) ◽  
pp. 309-314 ◽  
Author(s):  
M. H. Hsiao ◽  
E. J. Haug ◽  
J. S. Arora
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
State Space ◽  
The State ◽  
Programming Approach ◽  
Time Interval ◽  
Numerical Comparison ◽  
State Space Method ◽  
Continuous State ◽  
Space Method

A state space method of optimal design of dynamic systems subjected to transient loads is developed and applied. In contrast to the conventional nonlinear programming approach of discretizing the time interval and constructing a high dimension nonlinear programming problem, a state space approach is employed which develops the sensitivity analysis and optimization algorithm in continuous state space, resorting to discretization only for efficient numerical integration of differential equations. A numerical comparison of the state space and conventional nonlinear programming methods is carried out for two test problems, in which the state space method requires only one-tenth the computing time reported for the nonlinear programming approach.

scholarly journals Parameter and State Estimator for State Space Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ruifeng Ding ◽  
Linfan Zhuang
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
State Variables ◽  
Input Output ◽  
State Estimator ◽  
Output Data ◽  
Canonical State

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

scholarly journals Hysteresis-Based Current Control Approach by Means of the Theory of Switched Systems

2021 ◽  
Vol 11 (19) ◽  
pp. 9175
Author(s):  
Malte Thielmann ◽  
Florian Hans
Keyword(s):  
State Space ◽  
Switched Systems ◽  
Multiple Equilibria ◽  
Current Control ◽  
The State ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Reference Trajectory ◽  
State Variables ◽  
Control Approach

In this paper, a novel hysteresis-based current control approach is presented. The basis of the developed control approach is the theory of switched systems, in particular, the system class of switched systems with multiple equilibria. The proposed approach guarantees the convergence of the state trajectory into a region around a reference trajectory by selective switching between the individual subsystems. Here, the reference trajectory is allowed to be time varying, but lies within the state space spanned by the subsystem equilibria. Since already published approaches only show convergence to a common equilibrium of all subsystems, the extension to the mentioned state space is a significant novelty. Moreover, the approach is not limited to the number of state variables, nor to the number of subsystems. Thus, the applicability to a large number of systems is given. In the course of the paper, the theoretical basics of the approach are first explained by referring to a trivial example system. Then, it is shown how the theory can be applied to a practical application of a voltage source converter that is connected to a permanent-magnet synchronous motor. After deriving the limits of the presented control strategy, a simulation study confirms the applicability on the converter system. The paper closes with a detailed discussion about the given results.

scholarly journals Scrubbing During Learning In Real-time Heuristic Search

2016 ◽  
Vol 57 ◽  
pp. 307-343 ◽  
Author(s):  
Nathan R. Sturtevant ◽  
Vadim Bulitko
Keyword(s):  
State Space ◽  
Real Time ◽  
Lower Bounds ◽  
Heuristic Search ◽  
Search Algorithm ◽  
The State ◽  
Worst Case ◽  
Heuristic Search Algorithm ◽  
Practical Performance ◽  
Theoretical Results

Real-time agent-centered heuristic search is a well-studied problem where an agent that can only reason locally about the world must travel to a goal location using bounded computation and memory at each step. Many algorithms have been proposed for this problem and theoretical results have also been derived for the worst-case performance with simple examples demonstrating worst-case performance in practice. Lower bounds, however, have not been widely studied. In this paper we study best-case performance more generally and derive theoretical lower bounds for reaching the goal using LRTA*, a canonical example of a real-time agent-centered heuristic search algorithm. The results show that, given some reasonable restrictions on the state space and the heuristic function, the number of steps an LRTA*-like algorithm requires to reach the goal will grow asymptotically faster than the state space, resulting in ``scrubbing'' where the agent repeatedly visits the same state. We then show that while the asymptotic analysis does not hold for more complex real-time search algorithms, experimental results suggest that it is still descriptive of practical performance.

scholarly journals Best-First Heuristic Search for Multicore Machines

2010 ◽  
Vol 39 ◽  
pp. 689-743 ◽  
Author(s):  
E. Burns ◽  
S. Lemons ◽  
W. Ruml ◽  
R. Zhou
Keyword(s):  
State Space ◽  
Shared Memory ◽  
Temporal Logic ◽  
Heuristic Search ◽  
Multicore Processors ◽  
The State ◽  
New Method ◽  
Parallel Search ◽  
Empirical Comparison ◽  
Best First Search

To harness modern multicore processors, it is imperative to develop parallel versions of fundamental algorithms. In this paper, we compare different approaches to parallel best-first search in a shared-memory setting. We present a new method, PBNF, that uses abstraction to partition the state space and to detect duplicate states without requiring frequent locking. PBNF allows speculative expansions when necessary to keep threads busy. We identify and fix potential livelock conditions in our approach, proving its correctness using temporal logic. Our approach is general, allowing it to extend easily to suboptimal and anytime heuristic search. In an empirical comparison on STRIPS planning, grid pathfinding, and sliding tile puzzle problems using 8-core machines, we show that A*, weighted A* and Anytime weighted A* implemented using PBNF yield faster search than improved versions of previous parallel search proposals.

Furnace Modelling Using State Space Representation

2006 ◽  
Vol 3 (1) ◽  
pp. 37
Author(s):  
Razidah Ismail
Keyword(s):  
State Space ◽  
Power Plants ◽  
Controller Design ◽  
Cost Savings ◽  
Combined Cycle ◽  
The State ◽  
Space Representation ◽  
State Variables ◽  
State Space Representation ◽  
Space Modeling

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.

scholarly journals Subgoaling Techniques for Satisficing and Optimal Numeric Planning

2020 ◽  
Vol 68 ◽  
pp. 691-752
Author(s):  
Enrico Scala ◽  
Patrik Haslum ◽  
Sylvie Thiébaux ◽  
Miquel Ramirez
Keyword(s):  
State Space ◽  
Heuristic Search ◽  
State Of The Art ◽  
Planning Problem ◽  
State Variables ◽  
The Core ◽  
State Space Search ◽  
Theoretical Assumptions ◽  
Good Trade ◽  
Core Idea

This paper studies novel subgoaling relaxations for automated planning with propositional and numeric state variables. Subgoaling relaxations address one source of complexity of the planning problem: the requirement to satisfy conditions simultaneously. The core idea is to relax this requirement by recursively decomposing conditions into atomic subgoals that are considered in isolation. Such relaxations are typically used for pruning, or as the basis for computing admissible or inadmissible heuristic estimates to guide optimal or satis_cing heuristic search planners. In the last decade or so, the subgoaling principle has underpinned the design of an abundance of relaxation-based heuristics whose formulations have greatly extended the reach of classical planning. This paper extends subgoaling relaxations to support numeric state variables and numeric conditions. We provide both theoretical and practical results, with the aim of reaching a good trade-o_ between accuracy and computation costs within a heuristic state-space search planner. Our experimental results validate the theoretical assumptions, and indicate that subgoaling substantially improves on the state of the art in optimal and satisficing numeric planning via forward state-space search.

scholarly journals Furnace Modelling Using State Space Representation

2006 ◽  
Vol 3 (1) ◽  
pp. 37 ◽  
Author(s):  
Razidah Ismail
Keyword(s):  
State Space ◽  
Power Plants ◽  
Controller Design ◽  
Cost Savings ◽  
Combined Cycle ◽  
The State ◽  
Space Representation ◽  
State Variables ◽  
State Space Representation ◽  
Space Modeling

The state space modeling approach was developed to cope with the demand and performance due to the increase in system complexity, which may have multiple inputs and multiple outputs (MIMO). This approach is based on time-domain analysis and synthesis using state variables. This paper describes the development of a state space representation of a furnace system of a combined cycle power plant. Power plants will need to operate optimally so as to stay competitive, as even a small improvement in energy efficiency would involve substantial cost savings. Both the quantitative and qualitative analyses of the state space representation of the furnace system are discussed. These include the responses of systems excited by certain inputs and the structural properties of the system. The analysis on the furnace system showed that the system is bounded input and bounded output stable, controllable and observable. In practice, the state space formulation is very important for numerical computation and controller design, and can be extended for time-varying systems.

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