{"title":"联合机会约束动态规划","authors":"M. Ono, Y. Kuwata, B. Balaram","doi":"10.1109/CDC.2012.6425906","DOIUrl":null,"url":null,"abstract":"This paper presents a novel joint chance-constrained dynamic programming algorithm, which explicitly bounds the probability of failure to satisfy given state constraints. Existing constrained dynamic programming approaches cannot handle a joint chance constraint since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.","PeriodicalId":312426,"journal":{"name":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"Joint chance-constrained dynamic programming\",\"authors\":\"M. Ono, Y. Kuwata, B. Balaram\",\"doi\":\"10.1109/CDC.2012.6425906\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a novel joint chance-constrained dynamic programming algorithm, which explicitly bounds the probability of failure to satisfy given state constraints. Existing constrained dynamic programming approaches cannot handle a joint chance constraint since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.\",\"PeriodicalId\":312426,\"journal\":{\"name\":\"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CDC.2012.6425906\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 IEEE 51st IEEE Conference on Decision and Control (CDC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.2012.6425906","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper presents a novel joint chance-constrained dynamic programming algorithm, which explicitly bounds the probability of failure to satisfy given state constraints. Existing constrained dynamic programming approaches cannot handle a joint chance constraint since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step.