Predicate-Transformer Semantics of General Recursion

We develop the semantics of a language with arbitrary atomic statements, unbounded nondeterminacy, and mutual recursion. The semantics is expressed in weakest preconditions and weakest liberal preconditions. Individual states are not mentioned. The predicates on the state space are treated as elements of a distributive lattice. The semantics of recursion is constructed by means of the theorem of Knaster-Tarski. It is proved that the law of the excluded miracle can be preserved, if that is wanted. The universal conjunctivity of the weakest liberal precondition, and the connection between the weakest precondition and the weakest liberal precondition are proved to remain valid. Finally we treat Hoare-triple methods for proving correctness and conditional correctness of programs

The development of a weighted directed graph model for dynamic systems and application of Dijkstra’s algorithm to solve optimal control problems.

Master of Science (Chemical Engineering). University of KwaZulu-Natal. Durban, 2017.Optimal control problems are frequently encountered in chemical engineering process control applications as a result of the drive for more regulatory compliant, efficient and economical operation of chemical processes. Despite the significant advancements that have been made in Optimal Control Theory and the development of methods to solve this class of optimization problems, limitations in their applicability to non-linear systems inherent in chemical process unit operations still remains a challenge, particularly in determining a globally optimal solution and solutions to systems that contain state constraints. The objective of this thesis was to develop a method for modelling a chemical process based dynamic system as a graph so that an optimal control problem based on the system can be solved as a shortest path graph search problem by applying Dijkstra’s Algorithm. Dijkstra’s algorithm was selected as it is proven to be a robust and global optimal solution based algorithm for solving the shortest path graph search problem in various applications. In the developed approach, the chemical process dynamic system was modelled as a weighted directed graph and the continuous optimal control problem was reformulated as graph search problem by applying appropriate finite discretization and graph theoretic modelling techniques. The objective functional and constraints of an optimal control problem were successfully incorporated into the developed weighted directed graph model and the graph was optimized to represent the optimal transitions between the states of the dynamic system, resulting in an Optimal State Transition Graph (OST Graph). The optimal control solution for shifting the system from an initial state to every other achievable state for the dynamic system was determined by applying Dijkstra’s Algorithm to the OST Graph. The developed OST Graph-Dijkstra’s Algorithm optimal control solution approach successfully solved optimal control problems for a linear nuclear reactor system, a non-linear jacketed continuous stirred tank reactor system and a non-linear non-adiabatic batch reactor system. The optimal control solutions obtained by the developed approach were compared with solutions obtained by the variational calculus, Iterative Dynamic Programming and the globally optimal value-iteration based Dynamic Programming optimal control solution approaches. Results revealed that the developed OST Graph-Dijkstra’s Algorithm approach provided a 14.74% improvement in the optimality of the optimal control solution compared to the variational calculus solution approach, a 0.39% improvement compared to the Iterative Dynamic Programming approach and the exact same solution as the value–iteration Dynamic Programming approach. The computational runtimes for optimal control solutions determined by the OST Graph-Dijkstra’s Algorithm approach were 1 hr 58 min 33.19 s for the nuclear reactor system, 2 min 25.81s for the jacketed reactor system and 8.91s for the batch reactor system. It was concluded from this work that the proposed method is a promising approach for solving optimal control problems for chemical process-based dynamic systems

A Specific Network Link and Path Likelihood Prediction Tool

Communications have always been a crucial part of any military operation. As the pace of warfare and the technological complexity of weaponry have increased, so has the need for rapid information to assess battlefield conditions. Message passing across a network of communication nodes allowed commanders to communicate with their forces. It is clear that an accurate prediction of communication usage through a network will provide commanders with useful intelligence of friendly and unfriendly activities. Providing a specific network link and path likelihood prediction tool gives strategic military commanders additional intelligence information and enables them to manage their limited resources more efficiently. In this study, Dijkstra\u27s algorithm has been modified to allow the Queueing Network Analyzer\u27s (QNA) analysis output to act as a node\u27s goodness metric. QNA\u27s calculation of the expected Total Sojourn Time for the completion of queueing and service in a node provides accurate measurement of expected congestion. The modified Dijkstra\u27s algorithm in the Generalized Network Analyzer (GNA) is verified and empirically validated to properly deliver traffic. It appropriately generates the fastest traffic path from a start node to a destination node. This implementation includes notification if input parameters exceed the network\u27s processing capability. GNA\u27s Congestion Control displays notification and informs the user certain network input parameters must be lowered (PTR or BSTR) or where certain nodes must be improved to maintain node stability. With this unstable node identification, users can determine which node needs attention and improvements. Once this instability is removed, a good QoS is achieved and analysis proceeds