Consider a flying drone controlled from the ground by an observer who communicates with it via wireless. We are interested in how well the drone can be controlled via a channel that accepts r bits\/sec. Formally, the controller of a linear stochastic system aims to minimize a quadratic cost function in the state variables and control signal, known as the linear quadratic regulator (LQR). We characterize the optimal tradeoff between the communication rate r bits\/sec and the limsup of the expected cost b.<\/p>\n
We consider an information-theoretic rate-cost function, which quantifies the minimum mutual information between the channel input and output, given the past, that is compatible with a target LQR cost. We provide a lower bound to the rate-cost function, which applies as long as the system noise has a probability density function, and which holds for a general class of codes that can take full advantage of the memory of the data observed so far and that are not constrained to have any particular structure.<\/p>\n
Perhaps surprisingly, the bound can be approached by a simple variable-length lattice quantization scheme, as long as the system noise satisfies a smoothness condition. The quantization scheme only quantizes the innovation, that is, the difference between the controller’s belief about the current state and the encoder’s state estimate.<\/p>\n","protected":false},"excerpt":{"rendered":"
Consider a flying drone controlled from the ground by an observer who communicates with it via wireless. We are interested in how well the drone can be controlled via a channel that accepts r bits\/sec. Formally, the controller of a linear stochastic system aims to minimize a quadratic cost function in the state variables and […]<\/p>\n","protected":false},"featured_media":382982,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[13561,13546],"msr-video-type":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-382964","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-research-area-computational-sciences-mathematics","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/AclpFNc7Elw","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/382964","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":2,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/382964\/revisions"}],"predecessor-version":[{"id":808576,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/382964\/revisions\/808576"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media\/382982"}],"wp:attachment":[{"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/media?parent=382964"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=382964"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=382964"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=382964"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=382964"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=382964"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=382964"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=382964"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=382964"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/newed.any0.dpdns.org\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=382964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}