ɡˈɪvən ðɪs sˈɪstəm ðɪ ɑːbdʒˈɛktɪv ɪz tə fˈaɪnd ðə kəntɹˈoʊl ˈɪnpʊt hˈɪstɚɹi wˌɪtʃ æɾ ˈɛvɹi tˈaɪm mˈeɪ dᵻpˈɛnd lˈɪnɪɹli ˈoʊnli ɔnðə pˈæst mˈɛʒɚmənts sˈʌtʃ ðætðə fˈɑːloʊɪŋ kˈɔst fˈʌŋkʃən ɪz mˈɪnɪmˌaɪzd:
Given this system the objective is to find the control input history  which at every time  may depend linearly only on the past measurements  such that the following cost function is minimized: